Question

5. An investor would like to double their money. Their bank offers two interest rates. One rate will pay 9% interest compounded annually and one rate will pay 8.7% annually compounded continuously. Which one should you select and why? 6. A friend asks for a loan of money and offers to pay $20,000 at the end of 5 years. How much should you loan him now if you expect 15% interest per year on your loan?

Answer 1

5.

When there is 9% interest rate annually.

Let it takes n years to double the money.

2 = 1*(1+9%)^n

n = log 2 / log 1.09

n = 8.04 years

When there is 8.7% interest rate compounding continuously.

effective annual rate = e^.087 - 1 = 2.71828^.087 - 1 = 9.09%

Let it takes t years to double the money.

2 = 1*(1+9.09%)^t

t = log 2 / log 1.0909

t = 7.97 years

Since 8.7% interest rate compounding continuously takes lower time to double the money, then investor should opt for 8.7% interest rate compounding continuously to double the money.

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6.

Amount to be given as loan = 20000/(1+15%)^5

Amount to be given as loan = $9943.54 $9944