Question

After graduation, you receive a statement from your bank describing the total amount of your student loans and the terms for repayment. Your loans total $30,000 and will be repaid monthly over 8 years at an annual rate of 6%.

1. How much interest will you pay over the last 2 years of the loan?

2. What is your loan balance after 6 years?

Round to nearest dollar. Do NOT enter dollar signs.

3. If you make payments of $500 each month, how many years will it take to pay of the loan?

Round to the nearest year.

Answer 1

PV (loan amount) = 30,000; N (number of payments) = 8*12 = 96; rate (monthly rate) = 6%/12 = 0.5%, solve for PMT.

Monthly installment = 394.24

1). Principal outstanding at the end of 6 years: FV = 0; PMT = 394.24; N = 12*2 = 24; rate = 0.5%, solve for PV.

Principal outstanding = 8,895.25

So, in the remaining 2 years, principal of 8,895.25 will be paid out of the total 24 monthly installments.

Total interest paid over the last 2 years = (24*monthly installment) - principal outstanding

= (24*394.24) - 8,895.25 = 566.58 or 567

2). Loan balance after 6 years = 8,895.25 or 8,895 (as calculated above)

3). PV = 30,000; PMT = 500; rate = 0.5%, solve for NPER.

Number of installments = 71.51 or 71.51/12 years = 5.96 years or 6 years.