Question

Ricky Fowler needs to borrow $76,543 for seven years. The loan will be repaid in a single payment at the end of the loan term. Which one of the following interest rates is best for Ricky Fowler?

A.) 7.5% simple interest

B.) 7.6% simple interest

C.) 7.5% interest, compounded annually

D.) 7.75% interest, compounded annually

Answer 1

- Borrowed Amount = $76,543

The loan will be repaid in Single payment at the end of the loan term so calculating the Future value at the end of year 7 to determine which option is better for Ricky:-

A.) 7.5% simple interest

Future Value = Borrowed Amount*[1+ (r*n)]

where, r = Simple Interest rate = 7.5%

n = no of years = 7

Future Value = $76,543[1+(0.075*7)]

Future Value = $76,543(1+0.525)

Future Value = $116,728.08

B.) 7.6% simple interest

Future Value = Borrowed Amount*[1+ (r*n)]

where, r = Simple Interest rate = 7.6%

n = no of years = 7

Future Value = $76,543[1+(0.076*7)]

Future Value = $76,543(1+0.532)

Future Value = $117,263.88

C.) 7.5% interest, compounded annually

Future Value = Borrowed Amount*(1+r)^n

where, r = Interest rate compounded annually = 7.5%

n = no of periods = 7

Future Value = $76,543*(1+0.075)^7

Future Value = $76,543*1.65904914006

Future Value = $126,988.60

D.) 7.75% interest, compounded annually

Future Value = Borrowed Amount*(1+r)^n

where, r = Interest rate compounded annually = 7.6%

n = no of periods = 7

Future Value = $76,543*(1+0.076)^7

Future Value = $76,543*1.66988244574

Future Value = $127,817.81

As the Future Value is minimum in Part(A) 7.5% simple interest, thus 7.5% simple interest rates is best for Ricky Fowler

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