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Compound Interest: invested RM2500 into an account that pays 7% interest

by Sylvia Andrew
(Kota Kinabalu)











































Mr Amir invested RM2500 into an account that pays 7% interest compounded quarterly. He intended to keep the account untouched for five years, However, after three years he had to withdraw RM1000. Find the amount in his account after five years for the time he made his investment.

I'am confused if this question is refers to compound interest of simple interesn.

Comments for Compound Interest: invested RM2500 into an account that pays 7% interest

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Jul 28, 2011
Compound Interest
by: Staff


The question:

by Sylvia Andrew
(Kota Kinabalu)

Mr Amir invested RM2500 into an account that pays 7% interest compounded quarterly. He intended to keep the account untouched for five years, However, after three years he had to withdraw RM1000. Find the amount in his account after five years for the time he made his investment.

I'am confused if this question is refers to compound interest of simple interesn.



The answer:

The question refers to compound interest because the statement of the problem uses the term “compounded quarterly”.

To find the amount in his account after five years, it makes sense to break the problem into three parts: i) the first three years, ii) the RM1000 withdrawal, and iii) the last two years.


i) The first three years

7% compounded quarterly for the first 3 years

A = P*(1 + r)^t

A = final balance of the investment after the first 3 years
P = principle (the initial investment)
r = decimal form of quarterly interest rate
t = time in quarters

P = RM2500
r = 0.0175 (.07 is the decimal form of 7%. It is = 7÷100. r = the quarterly interest rate: .07/4 = 0.0175)
t = 12 quarters (4 quarters per year x 3 years = 12 quarters)


A (at 3 years) = P*(1 + r)^t

A (at 3 years) = 2500*(1 + 0.0175)^12

A (at 3 years) = 2500*(1.0175)^12

A (at 3 years) = 2500*(1.23144)

A (at 3 years) = RM 3078.6



ii) the RM1000 withdrawal

At the end of the third year (after the bank has paid the interest for 3 years), Mr. Amir withdraws RM1000.

Balance at the end of 3 years - Withdrawal = Beginning Balance for 4th year


RM 3078.6 - RM1000 = RM2078.6

Account Balance at the beginning of the 4th year = RM2078.6



iii) the last two years.


7% compounded quarterly for the last 2 years

A = P*(1 + r)^t

A = final balance of the investment after the first 3 years
P = principle (the initial investment)
r = decimal form of quarterly interest rate
t = time in quarters

P = RM2078.6
r = 0.0175 (.07 is the decimal form of 7%. It is = 7÷100. r = the quarterly interest rate: .07/4 = 0.0175)
t = 8 quarters (4 quarters per year x 2 years = 8 quarters)


A (at 5 years) = P*(1 + r)^t

A (at 5 years) = 2078.6*(1 + 0.0175)^8

A (at 5 years) = 2078.6*(1.0175)^8

A (at 5 years) = 2078.6*(1.14888)

A (at 5 years) = RM 2388.07



The final answer is: the amount in Mr. Amir’s account after five years = RM 2388.07



Thanks for writing.

Staff
www.solving-math-problems.com




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