Katrina has the option of an 8-year nonsubsidized student loan of $34,000 at an annual interest rate of 3.5% or an 8-year subsidized loan of $34,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.)
The total interest paid on the nonsubsidized loan is $ ?, and the total interest paid on the subsidized loan is $ ?
Therefore, Katrina will pay less interest on which loan?
To determine the total interest paid on each loan, we can use the formula for calculating the monthly payment of a loan:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
where:
P = principal amount of the loan
r = monthly interest rate (annual interest rate / 12)
n = total number of payments
For the nonsubsidized loan:
P = $34,000
r = 0.035 / 12 = 0.002917
n = 8 * 12 = 96 months
Monthly Payment = $34,000 * 0.002917 * (1 + 0.002917)^96 / ((1 + 0.002917)^96 - 1)
Monthly Payment = $442.74
Total Interest Paid = Total Payments - Principal
Total Payments = Monthly Payment * 96 months
Total Interest Paid = (Monthly Payment * 96) - $34,000
Total Interest Paid for the nonsubsidized loan = ($442.74 * 96) - $34,000
Total Interest Paid for the nonsubsidized loan = $42,461.04
For the subsidized loan:
P = $34,000
r = 0.045 / 12 = 0.00375
n = 8 * 12 = 96 months
Monthly Payment = $34,000 * 0.00375 * (1 + 0.00375)^96 / ((1 + 0.00375)^96 - 1)
Monthly Payment = $430.74
Total Interest Paid = (Monthly Payment * 96) - $34,000
Total Interest Paid for the subsidized loan = ($430.74 * 96) - $34,000
Total Interest Paid for the subsidized loan = $39,134.04
Therefore, Katrina will pay less interest on the subsidized loan, as the total interest paid is $39,134.04 compared to $42,461.04 for the nonsubsidized loan.