Question

You want to borrow $10,000 from a local bank, which is to be repaid in 2 equal semiannual
installments. The loan officer initially offered an interest rate of 12% compounded monthly.
However, you were able to negotiate that interest be compounded semiannually instead of
monthly. With this negotiation, how much do you save in total interest payments over the loan
life?

Answer 1

Compound interest formula:

FV = P (1+r/n)^(nt)

When interest is calculated as compounded monthly:

P = $10000, r = 12%, n = 1 year, t = 12 times

Putting all the values in the formula, we get:

Interest = $1268.25 and Loan amount to be repaid = $11268.25

When interest is calculated as compounded semiannually:

P = $10000, r = 12%, n = 1 year, t = 2 times

Interest = $1236 and loan amount to be repaid = $11236

Saving on interest (Difference) : 11268.25 - 11236 = 32.25