Alan Jackson invests $37,500 at 10% annual interest, leaving the money invested

Question

Alan Jackson invests $37,500 at 10% annual interest, leaving the money invested without withdrawing any of the interest for 10 years. At the end of 10 years, Alan withdraws the accumulated amount of money. Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually. Alan Jackson invests $37,500 at 10% annual interest, leaving the money invested without withdrawing any of the interest for 10 years. At the end of 10 years, Alan withdraws the accumulated amount of money. Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually.

Explanation / Answer

1.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence

A=$37500(1.1)^10

=$37500*2.59374246

=$97265.34

2.We use the formula:
A=P(1+r/200)^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence

A=$37500(1+10/200)^(2*10)

=$37500*2.653297705

=$99498.66(Approx).

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