Question

George invested $1,250 at the end of every month into an investment fund that was earning interest at 4.25% compounded monthly. He stopped making regular deposits at the end of 9 years when the interest rate changed to 4.50% compounded quarterly. However, he let the money grow in this investment fund for the next 4 years.

a. Calculate the accumulated balance in his investment fund at the end of 9 years

b. Calculate the accumulated balance in his investment fund at the end of 13 years

c. Calculate the amount of interest earned over the 13-year period.

Answer 1

- Amount Invested at the end of every month for 9 yaers = $1250

Interest rate for 9 years = 4.25% compounded monthly

a). Calculating the Accumulated Balance at the end of 9 years:-

Where, C= Periodic Payments = $1250

r = Periodic Interest rate = 4.25%/12 = 0.3541666%

n= no of periods = 9 years*12 = 108

Future Value = $164,101.62

So, the accumulated balance in his investment fund at the end of 9 years is $164,101.62

b). Interest rate chnaged to 4.50% compounded quarterly after 9 years.

Calculating the Accumulated Balance at the end of 13 years:-

Future Vaue at year end 13 = Future Vaue at year end 9*(1+r)^n

Where,

r = Periodic Interest rate = 4.50%/4 = 1.125%

n= no of periods = (13 years - 9 years)*4 = 16

Future Vaue at year end 13 = $164,101.62*(1+0.01125)^16

Future Vaue at year end 13 = $164,101.621.19601480026

Future Vaue at year end 13 = $196,267.97

So, the accumulated balance in his investment fund at the end of 13 years is $196,267.97

c). Total Interest Earned over 13 year period = Future Vaue at year end 13 - (No of payments*Periodic payments)

Total Interest Earned over 13 year period = $196,267.97 - (108*$1250)

Total Interest Earned over 13 year period = $61,267.97

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