Uses of compound interest – valuation of

securities, loans, instalment purchases,

savings and so on.

Time value of money – a ringgit today is

worth more than a ringgit tomorrow.

Simple interest – based on principal and

do not change.

Compound interest – based on principal

that changes from time to time because

of the interest added into principal.

Simple Interest Compound Interest

Based on original principal, total

amount in each period grows by

definite fraction from the principal.

Based on principal +interest that

grows from one interest interval to

another, total amount grows by

fraction of the sum of pincipal +

interest paid.

A linear function with respect to

time

Exponential function

RM1000 is invested for 3 years. Find the

interest received at the end of the 3

years if the investment earns 8%

compounded annually.

Consider this example:

Suppose RM9000 is invested for 7 years at 12% compounded quarterly.

The terms are :

- Original principal

- Annual nominal rate

- Interest period

- Frequency of conversions

- Periodic interest rate

- Number of interest periods in the investment period

Denoted by P, it is the original amount

invested. Based on the example, P =

RM9000

Denoted by k, interest rate for a year

together with frequency of conversions.

Based on the example, k = 12%

compounded quarterly.

Interest period is the length of time in

which the interest is calculated. Based

on the example, interest period is 3

months.

Denoted by m, number of times interest

is calculated for a year. Based on the

example, m = quarterly (means interest

calculated every three months) = 4.

Annually, m = 1

Semi-annually, m = 2

Monthly, m = 12

Daily, m = 360

Denoted by i, interest rate for each

interest period.

Based on the example : i = k/m = 12% /4=

3%

Denoted by n, number of times interest is

calculated during the investment period.

n = mt, m = frequency of conversions, t=

time in years

Based on the example, n = 4x7=28 times

Future value, or in simple interest, simple

amount

Compound interest, or the interest, I is

the difference between future value and

the original principal

Find the future value of RM1000 which

was invested for

a) 4 years at 4% compounded annually

b) 5 years 6 months at 14% compounded

semi-annually

c) 2 years 3 months at 4% compounded

quarterly

Find the future value for the following investments.

a) RM20000 at 5% compounded annually for 5 years

b) RM30000 at 6% compounded semi-annually for 5 years 6 months.

c) RM11500 at 8% compounded quarterly for

years

d) RM120 000 at 5% compounded monthly for

years

e) RM120 000 at 9% compounded daily for 270 days.

f) RM40 000 at 12% compounded every 4 months for 6 years

g) RM19 999 at 4.5% compounded every 2 months for 2 years.

Answer:

a) RM25 525.63 e) RM128 378.55

b) RM 41 527.02 f) RM 81 032.66

c) RM 14 298.80 g) RM 21 875.04

d) RM 141 126.15

RM9000 is invested for 7 years 3 months.

This investment is offered 12%

compounded monthly for the first 4 years

and 12% compounded quarterly for the

rest of the period. Calculate the future

value of this investment.

Answer: RM21 308.48

RM25 000 is invested for 4 years 9 months.

If the investment offered 12%

compounded semi-annually for the first 2

years and 10% compounded quarterly

for the rest of the period, find the future

value of this investment.

Answer: RM41 411.97

Lolita saves RM5000 in a savings account

which pays 12% interest compounded

monthly. 8 months later, she saved

another RM5000. Find the amount in the

account 2 years after her first saving.

Answer: RM12 211.57

Aris saved RM25 000 at 8% compounded

monthly. Two years later, he withdrew

RM14000 from the savings. Find the

amount left in the account.

Answer: RM15 322.20

How long does it take a sum of money to

double itself at 14% compounded

annually?

Answer: n=5.29 years

a.k.a discounted value

The present value means value of principal,P, which will yield the sum, S at the same interest rate after n interest periods.

This process is called discounting.

A debt RM3000 will mature in three years time. Find

a) The present value of this debt (RM1,999.03)

b) The value of this debt at the end of the first year (RM2,288.69)

c) The value of this debt at the end of four years (RM3,434.70)

Assuming money is worth 14% compounded semi-annually.

A debt of RM8000 will mature in 4 years’ time. Find

a) The present value of this debt

b) The value of this debt at the end of 2 years

c) The value of this debt at the end of 5 years.

assuming money is worth 9% compounded quarterly.

Answer:

a) RM5603.73

b) RM6695.51

c) RM8744.67

Imran opened a savings account which

offers an interest rate of 8%

compounded quarterly with an initial

deposit of RM2000. One and half years

later, he deposited RM3000 into the

same account. Find the amount

accumulated two and a half years after

the initial deposit.

Answer: RM5685.29

First Bank offers an interest of 7.5% compounded semi-annually while AZ Bank offers an interest of 7% compounded monthly.

a) Find the effective interest rate corresponding to the given nominal interest rate for each bank. If Ahmad wants to invest his money, which bank should he invests his money in? (7.64% , 7.23%, First Bank)

b) A man invests RM10,000 in AZ Bank for 5 and a half years. What is the amount of interest obtained when the investment period ends?(RM4679.71)

Fasha borrowed RM3000 at 6%

compounded semi-annually for four

years. Find the amount of interest

charged.

Answer: RM800.31