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Math Problem - Compound Interest











































RM10,000 was invested into an account at an interest rate of 6% compounded every three months.

a) Find the amount at the end of 2 years.

b) After two years the bank increased its interest rate to 8% compounded every three months. Find the amount at the end of five years of investment.

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Aug 05, 2011
Compound Interest
by: Staff

The question:

RM10,000 was invested into an account at an interest rate of 6% compounded every three months.

a) Find the amount at the end of 2 years.

b) After two years the bank increased its interest rate to 8% compounded every three months. Find the amount at the end of five years of investment.


The answer:


a) Find the amount at the end of 2 years.

6% compounded every three months (quarterly) for the first 2 years

A = P*(1 + r)^t

A = final balance of the investment at the end of 2 years
P = principle (the initial investment)
r = decimal form of quarterly interest rate
t = time in quarters (number of 3 month periods)

P = RM10,000
r = 0.015 (.06 is the decimal form of 6%. It is = 6÷100. r = the quarterly interest rate: .06/4 = 0.015)
t = 8 quarters (4 quarters per year x 2 years = 8 quarters)


A = P*(1 + r)^t

A (at 2 years) = 10,000*(1 + 0.015)^8

A (at 2 years) = 10,000*(1.015)^8

A (at 2 years) = 10,000*(1.12649)

A (balance at 2 years) = RM 11264.9



b) (the last 3 years) After two years the bank increased its interest rate to 8% compounded every three months. Find the amount at the end of five years of investment.

8% compounded every three months (quarterly) for the last 3 years

A = P*(1 + r)^t

A = final balance of the ?initial? investment of RM10,000 at the end of 5 years
P = principle (the value of the investment at the beginning of the last 3 year period)
r = decimal form of quarterly interest rate
t = time in quarters (number of 3 month periods)

P = RM 11264.9
r = 0.02 (.08 is the decimal form of 8%. It is = 8÷100. r = the quarterly interest rate: .08/4 = 0.02)
t = 12 quarters (4 quarters per year x 3 years = 12 quarters)


A = P*(1 + r)^t

A (at 5 years) = 11264.9*(1 + 0.02)^12

A (at 5 years) = 11264.9*(1.02)^12

A (at 5 years) = 11264.9*( 1.26824)

A (balance at 5 years) = RM 14286.6





The final answer is:

a) The amount at the end of 2 years = RM 11264.9

b) The amount at the end of five years of investment = RM 14286.6



Thanks for writing.

Staff
www.solving-math-problems.com


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