ordinary simple interest

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ENGINEEERING ECONOMICS

“The things which hurtinstruct.”

-Benjamin Franklin

I. SIMPLE INTEREST Ordinary Simple Interest

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SIMPLE INTEREST Exact Simple Interest

SIMPLE INTEREST Exact Simple Interest

Note:A year is a leap year if itis divisible by 4 anddivisible by 400 for acentennial year.(Centennial years are:1800, 1900, 2000, etc)

Sample Problem 1

Determine the ordinary simple interest on P5,000for 9 months and 10 days if the rate of interest is12%.

A. 857.14 B. 547.67 C. 687.33 D. 466.67

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Sample Problem 2

Jeffrey buys an electric fan from a merchant whoasks P1,250 at the end of 60 days (cash in 60days). Jeffrey wishes to pay immediately and themerchant offers to compute the cash price on theassumption that money is worth 8% simpleinterest. What is the cash price today?

A. 1,233.55 C. 987.56 B. 1,225.56 D. 1,325.56

Sample Problem 3

A man borrowed P10,000 from a loan firm at asimple interest of 15%. If the interest is to bededucted from the loan at the time the money isborrowed and at the end of 1 year he has to payback P10,000. Calculate the actual rate ofinterest.

A. 15.26% C. 12.14% B. 17.65% D. 11.23%

Sample Problem 4

Determine the exact simple interest on P10,000for the period from January 15 to June 20, 2004, ifthe rate of simple interest is 14%.

A. 600.54 B. 500.57 C. 850.54 D. 700.45

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Sample Problem 5

Determine the exact simple interest on P1,000 forthe period from January 10 to October 28, 2005 at12% interest.

A. 63.87 C. 85.75 B. 95.67 D. 56.47

II. RATES OF INTEREST Nominal Rate of Interest (NRI):

Nominal rate of interest specifies the rate of interest andthe number of interest periods per year.

Effective Rate of Interest (ERI):

Equivalent ratesFor two nominal rates to be equal, their effectiverates must be equal.

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Insert Problem

An interest rate is quoted as being 7.5%compounded quarterly. What is the effectiveannual interest rate?

A. 7.71%B. 7.81%C. 7.61%D. 7.91%

Sample Problem 6

Find the nominal rate compounded monthlywhich is equivalent to 12% compoundedquarterly.

A. 11.89% B. 10.57% C. 12.78% D. 12.67%

Sample Problem 7

If a nominal interest rate per year is 12%,andcompounding is continuous, what is theeffective interest rate per year?

A. 0.127% B. 11.275% C. 1.000% D. 12.75%

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III. COMPOUND INTEREST Future Worth, F:

Present Worth, P:

Where: (for both cases)

F = future worthP = Present worthi = Effective interest rate per

interest period (per month,per quarter, per year,etc)

n = Total number ofcompounding periods

m = mode of compoundingr = specified nominal ratet = number of years

For Continuous Compounding

Sample Problem 8

By the conditions of a will, the sum of P25,000 isleft to a girl to be held in trust by her guardianuntil it amounts to P45,000. When will the girlreceive the money if the fund is invested at 8percent compounded quarterly.

A. 6 years C. 7 years B. 8 years D. 9 years

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Sample Problem 9

What is the future worth of P12,000 deposited inan account earning interest at the rate of 9%compounded quarterly for 8 years.

A. 20,500.23 B. 25,400.56 C. 24,457.24 D. 23,642.56

Sample Problem 10

A man possesses a promissory note whosematurity value is P6700, due in 3 years hence. Ifthe rate of interest is 10% compounded semi-annually, what is the value of this note now?

A. 4,000 B. 3,000 C. 6,000 D. 5,000

Sample Problem 11

A P2,000 loan was originally made at 8% simpleinterest for 4 years. At the end of this period, theloan was extended for three years without theinterest being paid, this time at a rate of 10%compounded semi-annually. How much shouldthe borrower pay at the end of 7 years?

A. 3,574 C. 2,537 B. 3,537 D. 2,573

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Sample Problem 12

If P1,000 becomes P1,811.36 after 5 years wheninvested at an unknown rate of interestcompounded bimonthly, determine the unknownnominal rate and the corresponding effectiverate, respectively.

A. 6%, 12% C. 12%, 12.616% B. 10%. 10.562% D. 13%, 13.256%

Sample Problem 13

If the nominal interest rate is 3 percent, howmuch is P5000 worth in 10 years in acontinuously compounded account?

A. P6,350 B. P7,650 C. P8,500 D. P6,750

Sample Problem 14

How long will it take for an investment to doubleits amount if invested at an interest rate of 6%compounded monthly?

A. 10 years B. 12 years C. 13 years D. 14 years

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Sample Problem 15

How long will it take money to triple itself ifinvested at 8% compounded annually?


IV. AnnuitiesAnnuity is a series of equal payments “A” made atequal intervals of time..

Ordinary Annuity- the type of annuity where the payments are made at

the end of each period

Future Worth of Ordinary Annuity:

Present Worth of Ordinary Annuity:

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Deferred annuity- is the type of annuity where the first payment is made

later than the first or is made several periods after thebeginning of the annuity.

Future Worth of Deferred Annuity:

Present Worth of Deferred Annuity:

Annuity Due- is the type of annuity where the payment is made at

the beginning of each period

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Future Worth of Annuity Due:

Present Worth of Annuity Due:

Perpetuity- is an annuity in which the periodic payments

continue indefinitely.

Present Worth of Perpetuity:

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Sample Problem 16

How much money you invest today in order towithdraw P2000 annually for 10 years if theinterest rate is 9%?

A. 12,835.32 B. 12,785.45 C. 12,563.25 D. 12,586.47

Sample Problem 17

An employee obtained a loan of P10,000 at therate of 6% compounded annually to repair ahouse. How much must he pay monthly toamortize the loan within a period of ten years?

A. 110.22 C. 112.02 B. 125.25 D. 121.22

Sample Problem 18

Ernest invests P10,000 now for the collegeeducation of his 2- year old son. If the fund earns14% effective, how much will the son get eachyear starting from his 18th to the 22nd birthday?

A. 20, 894.23 C. 20,567.98 B. 20,791.64 D. 20,587.43

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Sample Problem 19

A farmer bought a tractor costing P25,000payable in 10 semi-annual payments starting atthe beginning of each period. If the interest rateis 26% compounded semi-annually, determinethe amount of each installment.

A. 5,047.30 C. 4,077.20 B. 4,654.21 D. 5,066.25

V. Capitalized CostsCapitalized Cost refers to the present worth of aproperty that is assumed to last forever. The capitalizedcost of any property is the “sum of the first cost andthe present costs of perpetual replacement,operation and maintenance”.

Capitalized Costs

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Capitalized Costs

Capitalized Costs

Sample Problem 20

A telephone company installed a new equipmentthat cost P150,000 and is estimated to have auseful life of 10 years. It is estimated to have ascrap value at the end of its useful life of P5,000.If the interest is 12% compounded annually,determine its capitalized cost.

A. P310,254.67 C. P281,425.76 B. P218,855.87 D. P301,425.76

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Sample Problem 21

A machine is purchased for P100, 000. If theannual maintenance cost is P18,000, determinethe capitalized cost of perpetual service with aninterest rate of 8%.

A. P325,000 B. P523,000 C. P235,000 D. P532,000

VI. DepreciationDepreciation is the decrease in the value of physicalproperty due to passage of time.

Methods of Computing Depreciation Straight Line Method

Straight line method of depreciation assumesthat the loss in value of the property is directlyproportional to the age of the property.

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Methods of Computing Depreciation Sinking Fund Method

Methods of Computing Depreciation Declining Balance Method

Methods of Computing Depreciation Double Declining Balance Method

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Methods of Computing Depreciation Sum – of – the - years – digits Method (SYD)

Sample Problem 22

An equipment costs P480,000 and has a salvagevalue of 10% of its cost at the end of its economiclife of 35,000 operating hours. In the first year, itwas used for 4,000 hours. Determine its bookvalue at the end of the first year using straightline method.

A. 430,629 C. 340,296 B. 403,269 D. 304,629

Sample Problem 23

A printing equipment costs P 73,500 has alife expectancy of 8 yrs. and has a salvagevalue of P 3500 at the end of its life. Thebook value at the end of “x” years is equal toP 38,500. Using straight line method ofdepreciation, solve for the value of “x”.


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Sample Problem 24

A broadcasting corporation purchased anequipment that costs P7,000, last 8 years and hasa salvage value of P350. determine the bookvalue during the 4th using declining balancemethod.

A. P1,711 C. P1,566 B. P5,166 D. P1,645

Sample Problem 25

A telephone company purchased a microwave radioequipment for P6M. Freight and installation chargesamounted to 3% of the purchase price. If the equipmentshall be depreciated over a period of 8 years with asalvage value of 5%, determine the depreciation chargeduring the fifth year using the sum of the years digitmethod.

A. 563,444.33 C. 635,333.33B. 653,333.33 D. 536,444.44

VIII. Break-even Analysis

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Sample Problem 26A manufacturer produces certain items at a labor costper unit of P315, material cost per unit of P100, and avariable cost of P3.00 per unit. If the item has a sellingprice of P995, how many units must be manufacturedeach month for the manufacturer to break even if themonthly overhead is P461,600.

A. 500 B. 700 C. 600 D. 800

ordinary simple interest

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