Question

In: Finance

Which of the following interest rates would be preferred by the borrower? A: 12% compounded annually....

Which of the following interest rates would be preferred by the borrower?

A: 12% compounded annually.

B: 11.75% compounded monthly.

C: 11.25% compounded daily (use a 360-day year).

Expert Solution

For example lets assume the amount borrowed is $ 1000

A

Interest when compounded annually = $ 1000 * 12%

= $ 120

B

If Interest Compounded Monthly

Interest = P * (1+r/12)^12*1 - P

= $ 1000 * ( 1+ 0.1175/12 )^12 - $ 1000

= $ 1000 * ( 1+ 0.009792)^12 - $ 1000

= $ 1000 * ( 1.009792)^12 - $ 1000

= $ 1000 * 1.124039 - $ 1000

= $ 1124.039 - $ 1000

= $ 124.039

C

If Compounded daily

Interest = P * (1+r/360)^360*1 - P

= $ 1000 * ( 1+ 0.1125/360 )^360 - $ 1000

= $ 1000 * ( 1+ 0.0003 )^360 - $ 1000

= $ 1000 * ( 1.000313 )^360 - $ 1000

= $ 1000 * 1.119053 - $ 1000

= $ 1119.053 - $ 1000

= $ 119.053

As the Interest amount is less in case of 11.25% daily compounding , this option is better for the borrower

Pls do rate, if the answer is correct and comment, if any further assistance is required.

jeff jeffy answered 2 years ago

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