You have an outstanding student loan with required payments of $500 per month for the next four

QUESTION

You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% APR (monthly). You are considering making an extra payment of $100 today (that is, you will pay an extra $100 that you are not required to pay). If you are required to continue to make payments of $500 per month until the loan is paid off, what is the amount of your final payment? What effective rate of return (expressed as an APR with monthly compounding) have you earned on the $100?
Solution: Amount of loan = A*(1-(1+i)^-n)/i i = Interest rate of period = .09/12 n = No of payments = 12*4 = 48 Loan amount = 500*(1-(1+.09/12)^-48)/(.09/12) = 20092 PV of 47 payments: =500*(1-(1+.09/12)^-47)/(.09/12) = 19743 Last

ayment = (20092 19743 100)*1+.09/12)^48 = 249 OR, can be rounded to 250 Effective rate of return earned = (1+APR/12)^12 1 = (1+.09/12)^12 1 = 9.38%

ANSWER:

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