3 Compound Interest

Compound Interest

- computed every compounding period

and as such accumulates money more

rapidly

Compound Amount and Present Value

Interest Period – refers to the time between two

successive conversions

Frequency of conversion (m) – refers to the

number of conversions periods in one year

Nominal rate (r) – annual interest rate

Interest rate per period ( i ) :

Number of conversions during the term (n) :

ri

m

( )n t m

Time should always express in years.

Conversion periods used for compound interest

computation are:

Conversion Period

Frequency of

Conversion (m)

Annually 1

Semi - annually 2

Quarterly 4

Monthly 12

Compound Amount Formula:

To find the present value:

1n

F P i

1

1

n

n

FP or P F i

i

Examples:

1. Determine the compound amount if

P12, 000 is invested at 10%

compounded quarterly for 5 years.

2. Mr. Torres wants to have P150, 000 in his

account at the end of 10 years. How much

should he invest today in a bank that pays 8%

compounded monthly?

#2/23. A man invested P8500 for 4 years

at 6% converted annually. What is the

accumulated amount?

#3/23. How much is the interest and the

accumulated amount of P25,000

invested at 3 years at 4% converted

quarterly?

#7/24. The day the boy was born, his

father invested P20,000 at 6%

converted semi-annually. Find the

value at the boy’s 18th birthday?

Compound Amount at a Fraction of a Period

n is assume to be integer

1n

F P i

If n is a fraction, compound amount can

be compute by following the two steps:

1. Find the compound amount at the end

of the largest number of whole periods

in the given time.

2. Accumulate the result in Step1 for the

remaining time using simple interest.

Examples:

1. Find the compound amount if P5, 000 is

invested for 3 years and 9 months at 12%

compounded semi –annually.

2. Find the interest and amount of P1.5M if it is

invested from October 28, 1972 to November

28, 2005 at compounded quarterly.

110 %

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