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VCEcoverageArea of studyUnits 3 & 4 • Business

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In thisIn this chachapterpter13A Simple interest13B Finding P, r and T13C Bonds, debentures and

term deposits13D Bank savings accounts13E Hire-purchase13F Effective rate of interest

13

Simple interest

Ch 13 FM YR 12 Page 607 Monday, November 13, 2000 3:28 PM

608

F u r t h e r M a t h e m a t i c s

Simple interest

People often wish to buy goods and services that they cannot afford to pay for at thetime, but which they are confident they can pay for over a period of time. The optionsopen to these people include paying by credit card (usually at a very high interest rate),lay-by (where the goods are paid off over a period of time with no interest charged butno access to or use of the goods until the last payment is made), hire-purchase, or aloan from the bank.

The last two options usually attract what is called

simple interest

. This is the amount ofmoney charged by the financial institution for the use of its money. It is calculated as apercentage of the money borrowed multiplied by the number of periods (usually years)over which the money is borrowed.

As an example, Monica wished to purchase a television for $550, but did not havethe ready cash to pay for it. She made an agreement to borrow the money from a bankat 12% p.a. (per year) simple interest and pay it back over a period of 5 years. Theamount of interest Monica would be charged on top of the $550 is

$550

×

12%

×

5 years which is $330.Therefore, Monica is really paying $550

+

$330

=

$880 for the television.


C h a p t e r 1 3 S i m p l e i n t e r e s t

609

Total amount of loan or investment

=

Initial amount or Principal

+

Interest(charged or earned)

A

=

P

+

I

It would have been more economical for Monica to buy the television for cash at thetime. However, by borrowing the money she has use of the television while she ispaying it off. Also, by using this method she would be paying a small amount eachmonth which is easy to budget for. The down-side is that she must pay the extrainterest.

Simple interest is the percentage of the amount borrowed or invested multiplied by the number of time periods (usually years). The amount is added to the principal either as payment for the use of the money borrowed or as return on money invested.

I

=

Simple interest charged or earned ($)

P

=

Principal (money invested or loaned) ($)

r

=

Rate of interest per period (% per period)

T

=

Time, the number of periods (years, months, days) over which the agreement operates

Hint

: The interest rate,

r

, and time period,

T

, must be stated and calculated in the same time terms, for example:

4% per annum for 18 months must be calculated over 1 years, as the interest

rate period is stated in years (per annum);1% per month for 2 years must be calculated over 24 months, as the interest rate period is stated in months.

IPrT100----------=

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Find the simple interest charged on borrowing $325 for 5 years at 3% p.a. (per annum or per year) interest.

THINK WRITE

Write the simple interest formula. I =

List the values of P, r and T. Check that r and T are in the same time terms.

P = $325r = 3% per yearT = 5 years

Substitute into the formula. I =

Use a calculator to evaluate. I = 48.75

Write your answer. The interest charged for borrowing $325 over5 years is $48.75.

1PrT100----------

2

3325 3 5××

100---------------------------

4

5

1WORKEDExample


610

F u r t h e r M a t h e m a t i c s

1. Transpose the formula for simple interest so that it

equals zero. (0

=

I

– ).

2. Press , choose

0: Solver

then press the up arrow key and enter the equation.

3. Press , then enter the values of the known variables and move the cursor to the variable to be solved for. The given values for worked example 1 are shown in the screen at right.

4. Press

[SOLVE]

.

Graphics CalculatorGraphics Calculator tip!tip! Simple interest calculations

PrT100----------

MATH

ENTER

ALPHA

Jan invested $210 with a building society in a fixed deposit account that paid 8% p.a. simple interest for 18 months. How much did she receive after the 18 months?

THINK WRITE


List the values of P, r and T. Check that r and T are in the same time terms. Need to convert 18 months into years.

P = $210r = 8% p.a.T = 18 months

= 1 years


Use a calculator to evaluate. I = $25.20Add the interest to the principal (total amount received).

A = P + IA = $210 + $25.20

Write your answer. Total amount received at the end of the investment is $235.20.

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C h a p t e r 1 3 S i m p l e i n t e r e s t 611

Simple interest

1 Find the interest charged on the following amounts borrowed for the periods and at the rates given.

2 Find the interest charged or earned on the following loans and investments:

a $690 loaned at 12% p.a. simple interest for 15 months

b $7500 invested for 3 years at 1% per month simple interest

c $25 000 borrowed for 13 weeks at 0.1% per week simple interest

d $250 invested at 1 % per month for 2 years.

3 Find the amount to which each investment has grown after the investment periodsshown in the following examples:

a $300 invested at 10% p.a. simple interest for 24 months

b $750 invested for 3 years at 1% per month simple interest

c $20 000 invested for 3 years and 6 months at 11% p.a. simple interest

d $15 invested at 6 % p.a. for 2 years and 8 months

e $10.20 invested at 8 % p.a. for 208 weeks.

a $680 for 4 years at 5% p.a. b $210 for 3 years at 9% p.a.

c $415 for 5 years at 7% p.a. d $460 at 12% p.a. for 2 years

e $1020 at 12 % p.a. for 2 years f $713 at 6 % p.a. for 7 years

g $821 at 7 % p.a. for 3 years h 11.25% p.a. on $65 for 6 years

i 6.15% p.a. on $21.25 for 9 years j 9.21% p.a. on $623.46 for 4 years

k 13 % p.a. on $791.35 for 5 years.

remember1. Simple interest is the percentage of an amount borrowed or invested multiplied

by the number of time periods, (usually years). The interest is added to the principal as payment for the use of the money or as return on the money invested.

2. A = P + I where A = Total amount ($)P = Principal, or amount borrowed or invested ($)I = Simple interest charged or earned ($)

3. I = I = Simple interest charged or earned ($)P = Principal (money invested or loaned) ($)r = Rate of interest earned per period (% per period)T = Time, the number of periods over which the

agreement operates

4. Interest rate, r, and time, T, must be stated and calculated in the same time terms.

PrT100----------

remember

13A

SkillSH

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Simpleinterest

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d

Simple interest

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612 F u r t h e r M a t h e m a t i c s

4If John had $63 in his bank account and earned 9% p.a. over 3 years, the simpleinterest earned would be:

5If $720 was invested in a fixed deposit account earning 6 % p.a. for 5 years, theinterest earned at the end of 5 years would be:

6A 4-year bond paid 7.6% p.a. simple interest. If Sonja bought a bond worth $550, theinterest she earned would be:

7Bodgee Bank advertised a special offer. If a person invests $150 for 2 years, the bankwill pay 12% p.a. simple interest on the money. At the expiry date, the investor wouldhave earned:

8Maclay invested $160 in a bank for 6 years earning 8% simple interest each year. Atthe end of the 6 years, he will receive in total:

9

Simple interest was calculated on a term deposit of 4 years at 3 % per year. When

Ashleigh calculated the total return on her investment of $63.50, it was:

10Joanne asked Sally for a loan of $125 to buy new shoes. Sally agreed on the conditionthat Joanne paid it back in two years at 3% p.a. simple interest. The amount Joannepaid Sally at the end of the two years was:

A $5.67 B $1701 C $17.01 D $22.68 E $27.00

A $234.00 B $23 400.00 C $23.40 D $216.00 E $350.00

A $16.72 B $167.20 C $717.20 D $1672 E $30.40

A $300 B $36 C $186 D $48 E $24

A $928 B $236.80 C $76.80 D $768 E $208

A $72.39 B $7.75 C $71.24 D $8.89 E $75.50

A $200 B $7.50 C $130.50 D $132.50 E $128.75

mmultiple choiceultiple choice

mmultiple choiceultiple choice12---






Ch 13 FM YR 12 12 Monday, November 13, 2000 3:28 PM


Betty invests $550 in an investment account earning 4% p.a. simple interest over6 years. Ron puts his $550 in a similar investment earning 5% p.a. simple interest for5 years. The difference in their earnings at the end of the investment period is:

12Two banks pay simple interest on short-term deposits. Hales Bank pays 8% p.a. over5 years and Countrybank pays 10% p.a. for 4 years. The difference between the twobanks’ final payout figure if $2000 was invested in each account is:

13 Robyn wishes to purchase a new dress worth $350 to wear to the school formal. If sheborrows the total amount from the bank and pays it off over 3 years at 11% p.a.simple interest, what is the total amount Robyn must pay back to the bank?

14 The Sharks Building Society offers loans at 8 % p.a. simple interest for a period of18 months. Andrew borrows $200 from Sharks to buy Monique an engagement ring.Calculate the amount of interest Andrew is to pay over the 18 months.

15 Silvio invested the $1500 he won in Lotto with an insurance company bond that pays12 % p.a. simple interest provided he keeps the bond for 5 years. What is Silvio’stotal return from the bond at the end of the 5 years?

16 The insurance company that Silvio used in the previous question allows people to with-draw part or all the money early. If this happens the insurance company will only pay6 % p.a. simple interest on the amount which is withdrawn over the period it was investedin the bond. The part which is left in the bond receives the original agreed interest. Silvioneeded $700 for repairs to his car 2 years after he had invested the money but left therest in for the full 5 years. How much interest did he earn from the bond in total?

17 Jill and John decide to borrow money to improve their boat, but cannotagree which loan is the better value. They would like to borrow $2550.Jill goes to the Big-4 Bank and finds that they will lend her the money at11 % p.a. simple interest for 3 years. John finds that the FriendlyBuilding Society will lend the $2550 to them at 1% per month simpleinterest for the 3 years.a Which institution offers the best rates over the 3 years?b Explain why.

A $55 B $5.50 C $7.50 D $0 E $595

A $0 B $800 C $2800 D $150 E $400



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Finding P, r and TIn many cases we may wish to find the principal, interest rate or period of a loan.In these situations it is necessary to rearrange or transpose the simple interestformula after (or before) substitution, as the following example illustrates.

Transposed simple interest formulaIt may be easier to use the transposed formula when finding P, r or T.

Simple interest formula transposes:

to find the principal

to find the interest rate

to find the period of the loan or investment

A bank offers 9% p.a. simple interest on an investment. At the end of 4 years the interest earned was $215. How much was invested?THINK WRITE


List the values of I, r and T. Check that r and T are in the same time terms.

I = $215r = 9% p.a.T = 4 years


215 =

Make P the subject by multiplying both sides by 100 and dividing both sides by (9 × 4).

P =

Use a calculator to evaluate. P = 597.22Write your answer. The amount invested was $597.22.

1PrT100----------

2

3P r T××

100----------------------

P 9 4××100

----------------------

4215 100×

9 4×------------------------

56

3WORKEDExample

P100 I×r T×

-----------------=

r100 I×P T×

-----------------=

T100 I×P r×

-----------------=



When $720 is invested for 36 months it earns $205.20 simple interest. Find the yearly interest rate.THINK WRITE/DISPLAY

Write the simple interest formula. r =

List the values of P, I and T. T must be expressed in years so that r can be evaluated in % per year.

P = $720I = $205.20T = 36 months

= 3 years

Substitute into the formula. r =

Evaluate on a calculator. Remember to bracket (720 × 3).

Write your answer. The interest rate offered was 9.5% per annum.

1100 I×P T×

-----------------

2

3100 205.20×

720 3×-------------------------------

4

5

4WORKEDExample

An amount of $255 was invested at 8.5% p.a. How long will it take, to the nearest year, to earn $86.70 in interest?THINK WRITE/DISPLAY

Write the simple interest formula. T =

Substitute the values of P, I and r. The rate, r is expressed per annum so time, T, will be evaluated in the same time terms, namely years.

P = $255I = $86.70r = 8.5% p.a.

Substitute into the formula. T =

Evaluate on a calculator. Remember to bracket (255 × 8.5).

Write your answer. The period of the investment was 4 years.

1100 I×P r×

-----------------

2

3100 86.70×

255 8.5×----------------------------

4

5

5WORKEDExample



Finding P, r and T

1 For each of the following, find the principal invested.a Simple interest of 5% p.a., earning $307 interest over 2 yearsb Simple interest of 7% p.a., earning $1232 interest over 4 yearsc Simple interest of 8% p.a., earning $651 interest over 18 monthsd Simple interest of 5 % p.a., earning $78 interest over 6 yearse Simple interest of 6.25% p.a., earning $625 interest over 4 years

2 For each of the following, find the interest rate offered. Express rates in % per annum.a Loan of $10 000, with a $2000 interest charge, for 2 yearsb Investment of $5000, earning $1250 interest for 4 yearsc Loan of $150, with a $20 interest charge, for 2 monthsd Investment of $1400 earning $178.50 interest for 6 yearse Investment of $6250 earning $525 interest for 2 years

3 For each of the following, find the period of time (to the nearest month) for which theprincipal was invested or borrowed.a Investment of $1000 at simple interest of 5% p.a. earning $50b Loan of $6000 at simple interest of 7% p.a. with an interest charge of $630c Loan of $100 at simple interest of 24% p.a. with an interest charge of $6d Investment of $23 000 at simple interest of 6 % p.a. earning $10 465e Loan of $1 500 000 at simple interest of 0.125% per month earning $1875

4 Lennie Cavan earned $576 in interest when she invested in a fund paying 9.5% simpleinterest for 4 years. How much did Lennie invest originally?

5 Lennie’s sister Lisa also earned $576 interest at 9% simple interest, but she only hadto invest it for 3 years. What was Lisa’s initial investment?

6 Jack Kahn put some money away for 5 years in a bank account which paid 3 %interest. He found from his bank statement that he had earned $66. How much didJack invest?

rememberWhen finding P, r or T:1. substitute the given values into the formula and then rearrange to isolate the

pronumeral, or2. transpose the simple interest formula

(a) to find the principal

(b) to find the interest rate

(c) to find the period of the loan or investment

and substitute the given values into the transposed formula.

P100 I×r T×

-----------------=

r100 I×P T×

-----------------=

T100 I×P r×

-----------------=

remember

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EET 13.3 WORKEDExample

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FindingP, rand T

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C h a p t e r 1 3 S i m p l e i n t e r e s t 6177 James needed to earn $225 in one year. He invested $2500 in an account earning

simple interest at a rate of 4.5% p.a. paid monthly. How many months will it takeJames to achieve his aim?

8 Carol has $3000 to invest. Her aim is to earn $450 in interest at a rate of 5% p.a. Overwhat term would she invest?

9Peter borrowed $5000 and intended to pay it back in 3 years. The terms of the loanindicated Peter was to pay 9 % p.a. interest. The interest Peter paid on the loan was:

10Joanne’s accountant found thatfor the past 2 years she hadearned a total of $420 interest inan account paying 6% simpleinterest. When she calculatedhow much she invested theamount was:A $350B $3500C $50.40D $7000E $70.00

11A loan of $1000 is taken over 5 years. The simple interest is calculated monthly. Thetotal amount repaid for this loan is $1800. The simple interest rate per year on thisloan is closest to:

12

Jarrod decides to buy a motorbike at no deposit and no repayments for 3 years. Hetakes out a loan of $12 800 and is charged at 7.5% p.a. simple interest over the3 years. The lump sum Jarrod has to pay in 3 years time is:

13Chris and Jane each take out loans of $4500 and are offered 6 % p.a. simple interestover a 3-year period. Chris’s interest is paid monthly whereas Jane’s is paid yearly.The difference in the total amount of interest each person pays after the 3 years is:

14 Alisha has $8900 that she is able to invest. She has a goal of earning at least $1100 in2 years or less. Do any of the following investments satisfy Alisha’s goal?a 10% p.a. for 15 monthsb 4 % p.a. earning $1200c After 100 weeks a final payout of $10 500d After 2 years at 0.6% per month

A $146 250 B $446.25 C $1462.50 D $121.88 E $1211.88

A 8.9% B 16% C 36% D 5% E 11.1%

A $960 B $13 760 C $2880 D $12 800 E $15 680

A none B $877.50 C $10 530 D $9652.50 E $1000


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Bonds, debentures and term depositsDebenturesIf a company needs money, one option is for it to offer a debenture (a legal documentdetailing an investment agreement) for sale to the public. An investor will pay anamount of money (principal) to the company, and in return the company agrees to paythe investor interest at regular intervals (monthly, quarterly or yearly). At the end of theagreed term the principal is returned to the investor. The advantage of the debenture istwo-fold: first, the company has the use of the money during the agreed period to makemore money for the company and second, the investor knows what their return will befor each period and is guaranteed the return of the principal.

Term deposits

Term deposits allow an investor to lend money to a bank or building society for aparticular length of time. The money cannot be withdrawn during the agreed period butearns a better interest rate than in a normal savings account. At the end of the term theinterest plus the principal is paid back to the investor. The advantage of the term depositis that the money is secure and the interest rate is better than that on a savings account.The disadvantage, of course, is that if the money is needed during the period it cannotbe withdrawn (except under special circumstances agreed to by the bank).

Investment bondsInvestment bonds are another form of investment which is offered to the investor by abank or the government, and interest is paid on the investment monthly, quarterly, sixmonthly or annually. The one advantage is that the bond can be sold to someone elseduring the period before the maturation date. This allows the investor some flexibility ifthe money is needed during the period of investment.

All the above investment types offer advantages to the investor and to the institution.The institution has the use of the money over a fixed period and the investor receiveshigher than normal interest. All of these investments carry some risk and individualsmust decide on which type to use based on personal circumstances.

Bonds, debentures and term deposits are simple interest accounts.

TOP INVESTOR RATES1 to 5 yr effective rates are shown in brackets. Source: CANNEX (Polifax 019 725 660).

BEST BANK TERM DEPOSITS BEST OTHERSPeriod30 days90 days180 days270 days1 year2 years3 years4 years5 years

BankHSBCArab BankHSBCArab BankSuncorp MetwayHSBC/PIBAHSBCHSBCHSBC

Rate4.705.005.125.255.005.66/5.706.206.166.33

(5.58)(5.78)(6.20)(6.30)(6.48)

Period30 days90 days180 days270 days1 year2 years3 years4 years5 years

InstitutionGIOGIOGIOGreater BS/HC CUGIOGIOAGCPolice CUAGC

Rate3.954.754.955.005.255.495.706.006.20

(5.35)(5.60)(5.82)(6.09)(6.34)



Jaclyn buys $50 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months:a calculate the amount of interest Jaclyn will earn for each quarterb calculate the total amount collected at the end of the term.THINK WRITE

a Write the simple interest formula. a I =

List the values of P, r and T. Convert the interest rate period to quarters.

P = $50 000r = 9.5% per year = 9.5% ÷ 4 per quarter= 2.375% per quarter

T = 1 quarter

Substitute into the formula and evaluate.

I =

= 1187.50Write your answer. Jaclyn will earn $1187.50 for each quarter.

b There are 6 quarters in 18 months. Alternatively, use the simple interest formula with the new data.

b Total interest = $1187.50 × 6= $7125

or

I =

= 7125Write your answer. The total interest earned is $7125.

1PrT100----------

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350 000 2.375 1××

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50 000 2.375 6××100

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Townbank offers a term deposit account paying investors 12.5% p.a. simple interest on investments over $100 000 for 2 years or more. Peta decides to invest $150 000 in this account for 2 years. How much interest will Peta earn at the end of the investment?

THINK WRITE


List the values of P, r and T. Check that r and T are described in the same time terms.

P = $150 000r = 12.5% p.a.T = 2 years


I =

= $37 500

Write your answer. Peta’s $150 000 invested for 2 years will earn $37 500.

1PrT100----------

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3 150 000 12.5 2××100

---------------------------------------------

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7WORKEDExample



Bonds, debentures and term deposits

1 Spice Clothing company offers debentures paying 8% p.a. interest paid quarterly for aperiod of 2 years. When $20 000 worth of Spice debentures are purchased, calculatethe total return on the investment.

2 Harry decided to invest $2000 in a term deposit for 18 months. The bank offered10.5% p.a. interest paid each half-year. Calculate the interest Harry would earn on theinvestment.

3 An investment bond is advertised as paying 10 % p.a. interest on a 3-year invest-ment. Elise purchased a bond for $3000, but needed to sell it after 18 months. Howmuch will Elise receive at the end of her 18-month investment?

4 Rabbit debentures, worth $10 000, were purchased for a period of 15 months. Thedebenture paid 12% p.a., payable each 3 months. What was the investment worth atthe end of the 15 months?

An investment bond is offered to the public at 9% p.a. Louise buys a bond worth $2000 that will mature in 2 years. How much in total will Louise receive at the end of the 2 years?THINK WRITE


List the values of P, r and T. P = $2000r = 9% p.a.T = 2 years


Use a calculator to evaluate. I = $360Add interest to principal. A = P + I

A = 2000 + 360= 2360

Write your answer. The $2000 investment bond will mature at the end of 2 years to a total of $2360 at simple interest of 9% p.a.

1PrT100----------

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32000 9 2××

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8WORKEDExample

remember1. Simple interest accounts include bonds, debentures and term deposits.2. Read the question carefully: does it ask for the interest or the final total

amount?

remember

13C

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Simpleinterest

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Simpleinterest

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GCpro

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Simpleinterest

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C h a p t e r 1 3 S i m p l e i n t e r e s t 6215 JNK Bank offers term deposits on amounts above $5000 at 12% p.a. simple interest

payable each quarter for periods longer than 2 years. Mr Smith invests $6000 in thisterm deposit for 2 years. What is Mr Smith’s final return on his money?

6 Mark purchases a $2500 investment bond earning 12 % p.a. interest paid yearly. The bond matures after 2 years. What interest will Mark earn?

7

Debentures in TRADEX are issued at 9% p.a. simple interest. The interest gained onan investment of $7000 over 3 years would be:

8

The rate of interest on a term deposit for 3 months is 4.25% per year. If $10 000 isinvested in the term deposit, the amount of interest earned over the 3 months is:

9

State government bonds pay interest of 7 % p.a. simple interest. Philippa invested$2500 in the bonds which mature in 5 years. Philippa’s income each quarter would be:

10

ElCorp offers company debentures earning 8 % p.a. interest for an investment of$5000 for 2 years. The interest on the investment is:

11

A term deposit is advertised stating that if $2500 is invested for 2 years the interestearned is $285. The rate of interest per annum is:

A $630 B $1890 C $18 900 D $7630 E $21 000

A $106.25 B $425 C $141.67 D $1062.50 E $1275

A $181.25 B $2718.77 C $45.31 D $725 E $72.50

A $170 B $212.50 C $825 D $850 E $85

A 10% B 17.5% C 5.7% D 11.4% E 10.5%

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12

An investment bond of $7500 pays interest of $1125 at 3.75% p.a. interest. The timethe bond is taken for is:

13

A principal amount is invested in a bond that will accumulate to a total of $64 365

after 4 months at 6 % p.a. The principal is:

14 The following term deposit rates were advertised in a magazine

15 Dennis and Delia have $7500 to invest. They know that they will need the money in18 months but are not sure how to invest it. While reading a magazine, they see thefollowing three advertisements:

i investment bonds offered at 12 % p.a. interest paid each 6 months

ii debentures in a company paying 12% p.a. with interest paid each quarter

iii a term deposit paying 11 % p.a. interest paid each 3 months.

a Calculate their total return on each investment.b What did you notice about the time in which the interest was calculated?

A 3 years B 4 years C 3 years D 4 years E 5 years

A $60 000 B $63 000 C $6300 D $50 000 E $5000

Term Rate

30–59 days 4.2% p.a.

60–149 days 4.7% p.a.

150–269 days 5.0% p.a.

270–365 days 5.4% p.a.


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Toni Ford had $5500 to invest. Calculate herreturn if she invested the money in a termdeposit with this bank for:a 35 daysb 120 daysc 1 year.Hint: Express days as a fraction of a year.

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Bank savings accountsMost banks offer their customers savings accounts with interest that is usually paid on 1. the minimum monthly balance, or2. the daily balance.

The interest is added at a specified time — say once or twice a year — as nominated by the bank, for example, on the first day of June and December of each year. The more frequently the interest is added, the better for the customers.

Savings accounts — minimum monthly balancesTo calculate interest on a minimum monthly balance saving account, the bank looks atthe balances of the account for each month and calculates the interest on the smallestbalance that appears in each month.

At the beginning of March, Ryan had $621 in his savings bank account. On 10 March he deposited $60. If the bank pays 8% p.a. interest paid monthly and calculated on the minimum monthly balance, calculate the interest Ryan earns in March.THINK WRITE

The smallest balance for March is $621, as the only other transaction in that month increased the balance.

Minimum monthly balance for March is $621.


List the values of P, with r and T in months.

P = $621

r = % per month

T = 1 month


I =

= 4.14Write your answer. The interest earned for the month of March

was $4.14.

1

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The minimum monthly balance method is used in the next worked example.

Savings accounts — daily balancesTo calculate the interest on a daily balance saving account, the bank looks at thebalances of the account. The number of days each balance is maintained is used tocalculate the interest. When doing these calculations for yourself, you need to set outyour workings carefully, for example using tables.

Let’s investigate worked example 10 again, using the daily balance method.

Minimum monthly balance method

The above passbook page shows the transactions for July. Find the interest that will be earned in July if the bank pays 7% p.a. simple interest on the minimum monthly balance.

Date Deposit Withdrawal Balance

3/7

7/7

21/7

28/7

$100

$500

$ 50

$678

$337.50

$837.50

$159.50

$209.50

THINK WRITE

To find the smallest balance for July, look at all the running balances. Also check balances at the start and end of the month. Notice that the balance on 1 and 2 July, if shown, would have been $237.50.

Minimum monthly balance for July is $159.50.


List the values of P, r and T in months. P = $159.50

r = % per month

T = 1 month

Substitute into the formula and evaluate. I =

= 0.93

Write your answer. The interest earned for July was $0.93.

1

2PrT100----------

3712------

4 159.50 712------ 1××

100------------------------------------

5

10WORKEDExample



The daily balance method offers more interest than the minimum monthly balance method, as it credits the customer for all monies in the account, including the $600 deposited for 14 days.

Daily balance methodUse the daily balance method to find the interest that will be earned in July, if the bank pays 7% p.a. simple interest on the daily balance.

THINK WRITE

Set up a table showing each new balance and the number of days the balance applies. Look at all running balances including those for 1 and 31 July.Calculate the interest for each balance. As the interest rate is in % per annum, express the number of days as a fraction of a year; for example, 2 days = of a year.

Sum the interest. The calculations were to hundredths of a cent for accuracy.

Interest for month = $2.9734

Round off to the nearest cent. $2.9734 ≈ $2.97Write your answer. The interest earned for July was $2.97.

1

Balance$

Number of days

the balance applies

Simple interest calculations

$

Interest earned

$

$237.50 2 $0.0911

$337.50 4 $0.2589

$837.50 14 $2.2486

$159.50 7 $0.2141

$209.50 4 $0.1607

237.50 7 2365---------××

100--------------------------------------

337.50 7 4365---------××

100--------------------------------------

837.50 7 14365---------××

100--------------------------------------

159.50 7 7365---------××

100--------------------------------------

209.50 7 4365---------××

100--------------------------------------

2

2365---------

3

45

11WORKEDExample

remember1. Two methods used by banks for calculating interest on savings accounts are:

(a) minimum monthly balances(b) daily balances.

2. Daily balances offer the best interest rate for investors.3. Look at the balances on the first and last day of the month when establishing

the minimum monthly balance or daily balances.4. Express days as a fraction of a year; for example, 1 day = of a year.1

365---------

remember



Bank savings accounts

1 A bank savings passbook showed that the opening balance for the month was $2150.That month Paul paid the following bills out of the account:Electricity $21.60 Telephone $10.30 Rent $52.00Paul also deposited his wage of $620 for the month into the account.a What was Paul’s minimum monthly balance?b If the bank pays 5.5% p.a. paid monthly on the minimum monthly balance, how

much interest did Paul earn in the month?

2

Roberta’s passbook shows the above transactions for May. Find the interest Robertawill earn in May if the bank pays 6% p.a. simple interest:a on the minimum monthly balanceb on the daily balance.

3 For the month of July, Rhonda received $3.20 in interest on her savings account.Rhonda’s minimum balance in July was $426.20. What was the per annum simpleinterest rate offered by the bank?

4 Kristen receives the following statement from her bank. Due to a computer error theinterest and balances were not calculated.Kristen rang the bank and was told that she received interest at a rate of 6 % p.a. paidmonthly on her minimum monthly balance. Copy out Kristen’s statement and fill in thebalances and interest payments.

Date Deposit Withdrawal Balance1/53/57/5

19/527/5

$12

$10

$16$ 8

$27.50$39.50$23.50$15.50$25.50

1998 Transaction Debit Credit Balance1 May Balance B/F 2132.203 May Cheq 4217 460.277 May Deposit 230.1617 May Cheq 4218 891.2026 May Wages 1740.6031 May Interest _______2 June Deposit 415.108 June Cheq 4220 2217.0019 June Cheq 4219 428.5021 June Cheq 4222 16.8023 June Wages 1740.6030 June Interest _______1 July Deposit 22.804 July Cheq 4221 36.7218 July Cheq 4223 280.9626 July Wages 1740.6031 July Interest _______

13D

GCpro

gram

Simpleinterest

WORKEDExample

9

EXCEL

Spreadsheet

Mathca

d

Simple interest

SkillSH

EET 13.4WORKEDExample

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WORKEDExample

11

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C h a p t e r 1 3 S i m p l e i n t e r e s t 6275 Using the bank statement from question 4, another bank offers to show Kristen that

daily balance interest credited each quarter is more rewarding. The interest is still6.75% p.a. but is only credited at the end of the quarter, that is, on 31 July. Calculate:a the interest for the quarter ending Julyb the increase in interest earned using the daily balance method.

Hint: This could be done using a spreadsheet. See the section on Spreadsheet Appli-cations later in this chapter.

6 Clark Kent has the following income and expenses for August and September.

Income: $1410.20 salary each fortnight beginning 4 August$461.27 income tax refund on 5 September$68.20 cheque from health fund on 10 August

Expenses: $620.80 rent on 20 August and 20 September$180.64 telephone account on 2 September$150.26 electricity account on 15 August$180.00 Visa account on 30 August$327.60 health fund on 5 August and 5 September

Draw up a statement (as for question 4) for Clark, remembering that he receives7 % interest paid on the last day of each month on the minimum monthly balance inthe account.

7 If the savings interest rate is 2 % p.a., calculate the interest credited at the end of eachquarter for the following accounts using:

i the minimum monthly balanceii the daily balance.

Also calculate:iii the increase in interest earned using the daily rather than the minimum monthly

balance method.a 3rd quarter statement for July, August and September

b 1st quarter statement for January, February and March in 2000

c

Date Deposit Withdrawal Balance3/77/8

21/828/820/9

$ 500$ 670

$10 000

$100

$420

$ 750.00$ 1250.00$ 1920.00$ 1500.00$11 500.00

Date Deposit Withdrawal Balance31/12/1999

1/2/20001/3/2000

28/3/2000

$100$600

$ 50$100

$400.00???

Date Deposit Withdrawal Balance3/10

17/1221/1222/1228/12

$2100$3500

$1900$400$650

$2450.00$5950.00$4050.00$3650.00$3000.00

12---

12---



Hire-purchase

A flat rate is the same as simple interest rate.

The interest charged is added onto the balance owing and then divided into the equalinstalments.

Advantages of this form of buying are:1. the purchaser has the use of the goods while paying them off2. the cost of the goods is spread over a long term in small amounts.The disadvantages are more complex:1. the purchaser pays more for the goods in the long run2. the goods are legally owned by the finance company until they are fully paid off3. any forfeit on making the regular payments entitles the finance company to repos-

sess the goods as well as retain all past payments made.

The main stages of hire-purchase interest and total price calculations are:Step 1. Check the price of the goods.Step 2. Pay any deposit.Step 3. Set up the balance as a loan.

Loan amount = price of goods − depositStep 4. Calculate the interest on the loan using the simple interest formula.Step 5. The total amount to be repaid is the sum of the balance and the interest.Step 6. Establish regular payments/instalments.

Instalment amount =

Step 7. Total cost of goods = deposit + loan amount + interestor = deposit + instalment amount × number of instalments

People buy on hire-purchase when they cannot afford to buy the goods for cash.A deposit is usually paid and the balance is paid over a fixed period of time. Theretailer arranges a contract with a financial institution and the purchaser paysregular instalments including interest at a flat rate to the financial institution.

total amountnumber of instalments-----------------------------------------------------



A sapphire ring with a marked price of $1800 is offered to the purchaser on the following terms: $200 deposit and the balance to be paid over 24 equal monthly instalments with interest charged at 11.5% p.a. flat rate. Find:a the total interest paidb the monthly repayments.

THINK WRITE

a Write the cash price. a Cash price = $1800Determine the deposit. Deposit = $200Calculate the amount of the loan required.

Balance or loan amount = cash price − deposit= $1800 − $200= $1600

List P, r and T. P = $1600r = 11.5% p.a.T = 2 years

Write the simple interest formula, substitute into it and evaluate.

I =

I =

I = $368Write your answer. Total interest to be paid is $368.

b Add the interest to the principal. b Total repayment amount = $1600 + $368= $1968

Calculate the monthly repayments. Regular payment =

=

= $82

Write your answer. The regular monthly repayments are $82.

1

2

3

4

5 PrT100----------

1600 11.5 2××100

--------------------------------------

6

1

2total amount

number of repayments------------------------------------------------------

$196824

---------------

3

12WORKEDExample



Weekly instalment advertisingMany retailers use the option of hire-purchase to attract new sales. They also choose toadvertise the instalment amount as it can seem to be very manageable. Buyers shouldinvestigate the entire arrangement offered and find answers to questions such as:1. What is the interest rate?2. How does it compare to bank rates?3. What is the total cost of the item?4. How much interest is charged?

A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a.a What is the monthly instalment? b What is the total cost of the car?THINK WRITEa Write the cash price. a Cash price = $21 000

Calculate the deposit, that is, 10% of $21 000.

Deposit = 10% × $21 000= $2100

Calculate the amount of the loan required.

Loan amount = $21 000 − $2100= $18 900

List P, r, and T. Check that r and T are in the same time terms. Convert the time period into years to match the % rate per annum.

P = $18 900r = 12% p.a.T = 60 months

= 5 years

Write the simple interest formula, substitute into it and evaluate.

I =

I =

I = 11 340Add the interest to the principal to find the total amount of the loan to be repaid.

Total amount = 18 900 + 11 340= $30 240

Calculate the monthly instalment. Regular payment =

=

= $504Write your answer. The monthly instalment is $504.

b Calculate the cost of the car. b Total cost = deposit + instalment amount× number of instalments

= 2100 + 504 × 60= $32 340

orTotal cost = deposit + loan + interest

= 2100 + 18 900 + 11 340= $32 340

Write your answer. The total cost of the car is $32 340.

12

3

4

5PrT100----------

18 900 12 5××100

-------------------------------------

6

7total amount

number of repayments------------------------------------------------------

$30 24060

-------------------

81

2

13WORKEDExample



The following advertisement for a computer was found in a newspaper.

If there is a total of 104 weekly instalments and a third deposit, find:a the interest chargedb the interest ratec the total cost of the computer.

THINK WRITE

a Write the cash price. a Cash price = $3695Calculate the deposit. Deposit = of $3695

= $1231.67Calculate the amount of the loan. Loan amount = $3695.00 − $1231.67

= $2463.33Calculate the total cost of the loan, that is, the total of the loan and the interest charged paid by weekly instalments.

Total cost of loan = $25.97 × 104= $2700.88

Calculate the interest charged and write your answer.

Interest charged = total amount − loanI = A − P

= 2700.88 − 2463.33= 237.55

Interest on the $2463.33 loan is $237.55b Use the transposed simple interest

formula to find r, the interest rate on the loan. Check that T is expressed in years to evaluate the interest rate in % per annum.

b P = $2463.33I = $237.55T = 104 weeks

= 2 years

r =

r =

= 4.82 . . .Write your answer. The interest rate for this hire-purchase is

4.8% p.a.c Calculate the total cost of the

computer.c Total cost = deposit + loan + interest

= 1231.67 + 2463.33 + 237.55= $3932.55

Write your answer. The total cost for the computer including interest on the loan is $3932.55.

1

213---

3

4

5

1

100 I×P T×

-----------------

100 237.55×2463.33 2×

-------------------------------

2

1

2

14WORKEDExample

Computer for sale

Cash price $3695or pay only a third deposit and

104 weekly instalments of only $25.97.



Hire-purchase

1 Debbie and Peter purchased a lounge suite on hire-purchase. The cash price was$2500. Peter and Debbie paid $250 deposit and signed an agreement to pay thebalance in 36 equal monthly instalments. If the hire-purchase company charges 14%p.a. simple interest, find:a the total interest paidb the monthly repayments.

2 When buying new appliances for a recently renovated kitchen, Cheryl bought, fromthe same supplier, a refrigerator worth $490, a stove worth $350 and a dishwasherworth $890. If she paid $450 deposit and paid the balance over 48 months in equalmonthly instalments at 12% p.a. simple interest, find:a Cheryl’s monthly instalmentsb the total amount Cheryl paid for the goods.

3 While on holidays in Noosa, Jan saw a bracelet she could not live without. Themarked price was $2000. The jewellery shop owner offered her a discount of 15% ifshe paid a deposit of $250. Jan paid the deposit and signed a hire-purchase agreementthat she would pay the balance of the bracelet’s cost at 15% p.a. flat rate with 24 equalmonthly instalments.a What was the price of the bracelet after the 15% discount?b Calculate the balance Jan was to pay back.c Calculate the interest Jan paid.d Calculate Jan’s monthly instalment.e How much did Jan pay altogether for the bracelet?

4 The cash price of a suit is $1800. If a customer pays a deposit of $300 and pays equalmonthly instalments of $60 over 2 years, calculate:a the amount of interest chargedb the flat rate of interestc the total paid for the suit.

5 A car has a marked price of $7500. The dealer gives two choices of payment:i no deposit, with the $7500 paid in equal monthly instalments of $250 for 3 yearsii $1500 deposit, paying interest of 12% p.a. and making equal monthly repayments

for 3 years.a Calculate the interest rate in choice i.b Which deal is best for the purchaser? Why?

rememberThe main stages of interest and total price calculations are:1. Loan amount = price of goods − deposit2. Flat rate interest on the loan is calculated using the simple interest formula.

3. Instalment amount =

4. Total cost of goods = deposit + loan amount + interestor = deposit + instalment amount × number of instalments


remember

13EWORKEDExample

12

WORKEDExample

13

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1412---



An electric guitar is bought on hire-purchase for a $250 depositand monthly instalments of $78.50 for 3 years. The cash pricefor this guitar is $2500. The interest rate is closest to:

7‘Carpeting the home is not cheap’, Rob stated.‘Hire-purchase is the answer’, replied Tom.The cost of the carpet for the house is $9500. Rob and Tom place a deposit of $1500 and plan to pay it back weekly over 4 years at 13% interest per year. The weekly instalment is:

8A salesman told a couple that if they bought a television at $890 today, he wouldallow a deposit of $100 plus $8.65 weekly for 2 years. The interest rate charged is:

9 For the video camera in the advertisement, find:i the total paidii the interest rate for both Option a and Option b.

10 A company advertised a dining room suite for $2500. You could pay:a cash and receive a 10% discount, orb $200 deposit and 5% p.a. interest on the remainder for 3 years, orc $300 deposit and 4.5% p.a. on the remainder for 3 years, ord $400 deposit and 4% p.a. interest on the remainder for 4 years.What is the total paid on each deal?

11 Carefully read the advertisement at right forthe cash price and regular instalments for thecolour television. The term of the repaymentsis for 3 years with 20% deposit. Calculate:a the flat interest rateb the total cost of the TV under the hire-

purchase planc the increase in cost over a cash sale.

$1095 or $15.40 fortnightly

A 9.5% B 7% C 8.5% D 8% E 7.5%

A $253.37 B $62.20 C $46.20 D $58.46 E $462.00

A 10% B 7% C 6.5% D 9 % E 7.5%




12---

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12---



Effective rate of interest

When purchasing goods on hire-purchase or through a personal loan, the financecompany lending the money hopes to make the deal look as attractive as possible.Some details, therefore, are not prominently stated to the customer. One such detailis the effective rate of interest. The amount borrowed reduces over the term of theloan, but the customer is still paying interest on the total initial loan amount. Theeffective interest rate is the equivalent reducing balance interest rate taken over thecontract period.

There are two ways of converting flat rate to effective rate.1. Estimation

Effective interest rate is a little less than 2 × flat interest rate.2. Calculation

Effective interest rate = × flat rate where n is the number of payments.

That is, on a loan of $100 at 10% interest over 4 years with yearly repayments, theinterest charged is:

I = 100 × 0.10 × 4 = $40.

The effective interest rate is × 10% = 16% (assuming yearly repayment).

This means that, even though the person is paying $40 interest, the effective interestrate over the period is actually 16%, not 10%. The longer the period of the loan, thehigher the effective interest rate. This is shown clearly in the following table.

Total interest $40 Flat rate 10% Effective rate 16%

YearPrincipal

owingRepayment of principal

Flat rate ofinterest paid

Effective rate ofinterest paid

1 100 25 10% of 100 = 10 16% of 100 = 16

2 75 25 10% of 100 = 10 16% of 75 = 12

3 50 25 10% of 100 = 10 16% of 50 = 8

4 25 25 10% of 100 = 10 16% of 25 = 4

$100 $40 $40

$10,000P E R S O N A L L O A N

$149

Based on a 3 year term at a fixed rate of 9.95%* p.a.

from per fortnight

2nn 1+------------

2 4×4 1+------------



Jason decides to borrow money for a holiday. If a personal loan is taken over 4 years with equal quarterly repayments at 12% p.a. flat rate (simple interest), calculate the effective rate of interest.

THINK WRITE

Write the flat rate and number of instalments.

Flat rate = 12%n = 4 × 4

= 16

Write the formula for effective rate of interest.

Effective rate = × flat rate

Substitute n = 16 and r = 12. Effective rate =

= 22.588Write your answer. Check the answer by estimating the rate which is less than 2 × 12% (or 24%) p.a.

The effective interest rate is 22.6% p.a. for a flat rate loan of 12% with sixteen instalments.

1

22n

n 1+------------

32 16×16 1+--------------- 12×

4

15WORKEDExample

remember1. The effective interest rate is a true indication of the interest rate on a loan that

is calculated using a flat interest rate when the loan is progressively being reduced, such as in hire-purchases.

2. Estimation of effective interest:Effective interest rate is a little less than 2 × flat interst rate.

Calculation of effective interest:


3. The fewer the payments, the closer the flat rate is to being a true indication of the rate charged.For example, 12% flat rate with 1 payment only:

Effective rate = × 12% = 12%

2nn 1+------------

2 1×1 1+------------

remember




1 William is to purchase a new video recorder. If William pays $125 monthly instalmentsover 3 years at an interest rate of 11.5% p.a. simple interest, what effective interest rateis he paying?

2

For each of the items in the above table, calculate:i the total amount of interest charged on each itemii the total amount paid over the period given for each itemiii the monthly instalment on each itemiv the effective interest rate.

3 The cash price for a car is $4600. If the car is purchased on time payments the cost willbe $5200. A deposit of $100 is required and the agreement is that the car will be fullypaid for in 3 years, paid in equal monthly instalments. Find:a the monthly instalmentb the simple (flat) interest rate per yearc the effective interest rate.

4 A camera valued at $1200 is purchased using a hire-purchase agreement. A deposit of$200 is required and equal monthly instalments of $75 are paid over the 18-monthagreed period. Calculate:a the flat (simple) interest rate per annumb the effective interest rate.

5 The bank approves a personal loan of $5000. A flat interest rate of 12.5% p.a. ischarged, with repayments to be made over a 9-month period in equal weekly instal-ments. Calculate:a the weekly instalmentb the effective interest rate.

6 Calculate the effective interest rate on a loan of $1000 if the monthly repayments are$60 and the loan is to be repaid over 2 years. (Hint: First calculate the simpleinterest rate.)

Item

Cash price

$Deposit

$

Monthly instalment

$Interest

rateTerm of

loan

a Television $875 $150 8% p.a. 2 years

b New car $23 990 $2000 10% p.a. 5 years

c Clothing $550 $100 7.5% p.a. 1 year

d Refrigerator $1020 $50 6 % p.a. 18 months

e Tools $250 $75 9% p.a. 15 months

13FWORKEDExample

15

EXCEL

Spreadsheet

Mathca

d


34---


C h a p t e r 1 3 S i m p l e i n t e r e s t 6377 Carefully read the advertisement (including the small print) for the purchase of the

refrigerator below and calculate:a the flat interest rateb the effective interest ratec the total cost under the hire-purchase pland the increase in cost over a cash sale.

8 Copy and complete the following table.

Cash price Deposit

Instalment (monthly) Period

Simple interest

rate

Effective interest

rate

$2500 $500 2 years 10% p.a.

$150 $50 6 months 9.5% p.a.

$685 $75 9 months 6 % p.a.

$128 $ nil $11.20 1 year

$6500 $500 $325 2 years

$10 000 $1500 5 years 10% p.a.

$599or

$4.21weekly

(one third depositover two years)

WorkS

HEET 13.2

34---



Spreadsheet applications

Accountants, financial planners, banks and other financial institutions use spreadsheetsto record and perform calculations. Many calculation tasks are similar in nature andtedious; therefore, once a spreadsheet is set up, some of these tasks can be done morequickly and easily. Another advantage of the use of a spreadsheet is solving the ‘whatif’ question. This function allows the numbers entered on the spreadsheet to be changedand an answer to be calculated to predict what would happen in a particular scenario.This is particularly useful when looking at factors such as how much a person canborrow and pay back, changes in terms, and changes in interest rates.

Your Maths Quest CD contains the Excel files ‘Simple interest’ and ‘Effective rate ofinterest’. These may be used to investigate various scenarios by typing new values inthe yellow cells or by modifying the spreadsheet in some way. A screen shot of the file‘Simple Interest’ is shown below.

Which is the best deal?1 Find three advertisements that offer products on hire purchase.2 Investigate each offer by calculating:

a the total amount of interest to be paidb the total amount to be paid over the term of the loanc the monthly repaymentd the effective interest rate.

3 Compare this with other methods of financing the purchase of the product.4 Write a brief report on the advantages and disadvantages of each method.

EXCEL

Spreadsheet

Simpleinterest

EXCEL

Spreadsheet

Effectiverate ofinterest



Simple interest formula• A = P + I where A = Total amount ($)

P = Principal or amount borrowed or invested ($)I = Simple interest charged or earned ($)

• I = I = Simple interest charged or earned ($)P = Principal (money invested or loaned) ($)r = Rate of interest earned per period (% per period)T = Time, the number of periods over which the agreement operates

• Interest rate, r, and time period, T, must be stated and calculated in the same time terms.

Finding P, r and T• To find the principal P =

• To find the interest rate r =

• To find the period of the loan or investment T =

Bonds, debentures and term deposits• Term investments with governments are called bonds.• Term investments with companies are called debentures.• Term investments with banks are called term deposits.• All three are investments for a fixed period of time offering a simple interest rate.

Savings banks — minimum monthly and daily balances• Two methods used by banks for calculating interest on savings accounts are:

1. minimum monthly balances 2. daily balances.• Daily balances offer the best interest rate for investors.• Look at the balances on the first and last day of the month when establishing the

minimum monthly balance or daily balances.• Express days as a fraction of a year; for example, 1 day = of a year.

Hire-purchase• Hire-purchase is a loan for goods with interest calculated using flat rate (simple)

interest and regular payments.• The main stages of calculations are:

1. Loan amount = price of goods − deposit2. Flat rate interest on the loan is calculated using the simple interest formula.

Instalment amount =

Total cost of goods = deposit + loan amount + interest or= deposit + instalment amount × number of instalments

Effective rates of interest• The effective interest rate is a true indication of the interest rate on a loan. It is

calculated using a flat interest rate when the loan is progressively being reduced, such as in hire-purchases.1. Estimation:

Effective interest rate is a little less than 2 × flat interest rate2. Calculation:


summary

PrT100----------

100 I×r T×

-----------------

100 I×P T×

-----------------

100 I×P r×

-----------------

1365---------


2nn 1+------------



Multiple choice

1 Two banks pay simple interest on short-term deposits. Bank A pays 6% p.a. over 4 years and

Bank B pays 6.5% p.a. for 3 years. The difference between the two banks’ final payout

figure if $5000 was invested in each account is:

2 Clayton invested $360 in a bank for 3 years at 8% simple interest each year. At the end of the 3 years, the total amount he will receive is:

3 Philip borrowed $7000 and intended to pay it back in 4 years. The terms of the loan indicated Philip was to pay 9% p.a. interest. The interest Philip paid on the loan was:

4 A loan of $5000 is taken over 5 years. The simple interest is calculated monthly. The interest bill on this loan is $1125. The simple interest rate per year on this loan is:

5 The principal invested in an investment bond that will accumulate $2015 after 6 months

invested at 6 % p.a. is:

6 A loan of $10 000 is taken over 10 years. The total interest bill on this loan is $2000. The simple interest rate per year on this loan is:

7 A 6-year bond pays 8 % p.a. simple interest. If Rhonda buys a bond worth $500, the

interest she would earn would be:

8 Simple interest was calculated on a term deposit of 5 years at 3 % p.a. When Leigh

calculated her total return on her investment principal of $350, her return was:

9 State government bonds pay interest of 7 % p.a. simple interest. Jess invested $3500 in the

bonds which mature in 5 years. Jess’s income each quarter would be:

A $0 B $1200 C $1137.50 D $150 E $62.50

A $86.40 B $236.80 C $28.80 D $388.80 E $446.40

A $25 200 B $630 C $7630 D $9520 E $2520

A 3% B 4 % C 3.75% D 5% E 3.5%

A $60 000 B $62 000 C $6200 D $50 000 E $5000

A 3% B 4 % C 2% D 5% E 2.5%

A $250 B $255 C $2550 D $233.75 E $230

A $415.63 B $400 C $65.63 D $131.25 E $481.25

A $113.00 B $1356.25 C $3567.81 D $67.81 E $82.50

CHAPTERreview

13A12---

13A

13A

13B12---

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13C12---

13C34---

13C34---


C h a p t e r 1 3 S i m p l e i n t e r e s t 64110 In the bank statement shown below the minimum balance for the month is:

11 A pearl necklace is purchased on hire-purchase for $225 deposit with equal monthly payments of $80 for 2 years. The cash price is $2000. The interest rate is:

12 A hire-purchase contract specifies that there are to be monthly payments for 2 years. The flat rate of interest is 6.3% p.a. The effective interest rate for this contract is closest to:

Short answer1 Cynthia invested $270 with a building society in a fixed deposit account that paid 8% p.a.

simple interest for 4 years. How much did Cynthia receive at the end of the 4 years?

2 A bank offers 8.5% p.a. simple interest on an investment. At the end of 3 years the interest earned was $765. How much was invested?

3 If $725 is invested for 3 years and earns $206.65 interest, calculate the yearly interest rate.

4 Jack put some money away for 4 years in a bank account which is paying 3 % p.a.

interest. He found on his bank statement he had earned $67.50. How much did Jack invest?

5 Jacob needed to earn $225 in one year. He invested $2000 in an account earning simple interest at a rate of 4.5% p.a. paid monthly. How many months will it take Jacob to achieve his aim?

Date Transaction Deposit Withdrawal Balance

5/4

7/4

9/4

23/4

Transfer from CBR

Salary

Cheque — 23456

ATM — Rowville

$100

$1500

$1380

$125

$456.50

$1956.50

$576.50

$451.50

A $456.50 B $1956.50 C $576.50 D $451.50 E $356.50

A 3.5% B 6% C 4% D 8% E 7.5%

A 12.1% B 11.6% C 8.4% D 6.3% E 12.6%

13D

13E

13F

13A

13B

13B13B

12--- 3

4---

13B



6 Steve invested the $1800 he won at the races in an insurance company bond that pays 12 % p.a. provided he keeps the bond for 4 years. What is Steve’s total return from the bond at the end of the 4 years?

7 Jocelyn buys $3500 worth of debentures in a company. She earns 8.5% p.a. simple interest paid to her quarterly. If the agreed period of the debenture was 28 months, calculate the amount of interest Jocelyn will earn.

8 The bank offers a term deposit account paying investors 10.5% p.a. on investments over $10 000 for 2 years. Paul decides to invest $12 000 in this account. How much interest will he earn at the end of the investment?

9 An investment bond is offered to the public at 10% per year. Louis buys a bond worth $4000 that will mature in 2 years. How much in total will Louis receive at the end of the 2 years?

10 At the beginning of July, Ross had $580 in his savings bank account. On 15 July he withdrew $80. If the bank pays 8% p.a. interest paid monthly, calculate the interest Ross earns in July:a if calculated on the minimum monthly balanceb if calculated on the daily balance.

11

Deborah’s passbook shows the above transactions for May. Calculate the interest Deborah will earn in May if the bank pays 4 % p.a. simple interest monthly:a on the minimum monthly balanceb on the daily balance.

Date Deposit Withdrawal Balance

1/53/57/5

19/527/5

$12$6

$28.80

$10

$302.20$273.40

13C12---

13C

13C

13C 12--- 1

2---

13D

13D

34---


C h a p t e r 1 3 S i m p l e i n t e r e s t 64312 The cash price of a car is $18 000.

If a customer pays a deposit of $3000 and pays equal monthly instalments of $300 over 5 years, calculate:a the amount of interest chargedb the flat rate of interestc the total paid for the card the effective interest rate.

13 The cash price for a bicycle is $460. If the bike is purchased on time payments the total cost will be $550. A deposit of $50 is required and the agreement is that the bike will be fully paid for in 2 years, in equal monthly instalments. Find:a the monthly instalment

(round up to the nearest cent)b the simple interest rate per year

(to 1 decimal place)c the effective interest rate

(to 1 decimal place).

13E, F

13E, F



Analysis

1

a Complete the missing credits, debits and balances in the shaded areas of the above account.b The bank is offering 2.4% p.a. on the minimum monthly balance. What is the interest rate

per month?c Calculate the interest that was earned for the month of August.

2 Geoff wants to buy a windsurfer. Its retail price is $3995. Geoff’s first option for financing the purchase is using hire-purchase. The terms offered by Your Money Finance Company is 10% deposit with fortnightly instalments over 2 years at an interest rate of 7.8% per annum.a How much will Geoff need to withdraw from his savings account to pay the deposit?b Calculate the fortnightly repayments and total interest charge.c What is the total cost of the windsurfer?d A personal loan is advertised at 13.5% per annum. For Geoff to compare the interest rate

he needs to convert the hire-purchase flat rate of interest to the effective interest rate. Calculate the effective interest rate.

3 Another option is for Geoff to save up until he has the cash to pay for the windsurfer. He can place the balance of his savings account (shown above in question 1) into a term deposit offering 5.6% per annum for a 2-year term.a Calculate the total value of his investment at the end of 2 years.b Geoff uses the term deposit investment towards the purchase of the windsurfer. What extra

fortnightly savings will be needed over the next 2 years to make up the balance of $3995?c What is the main attraction of the hire-purchase option over the options in 3a and b?

Date Description Debit Credit Balance

4 August8 August19 August27 August28 August

ATMDepositEFTPOSSalaryATM

100.00

119.501527.40

325.60975.60

2383.501983.50

testtest

CHAPTERyyourselfourselftestyyourselfourself

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