You take out the following student loans for your education, $10,000 on 1/1/2013

Question

You take out the following student loans for your education, $10,000 on 1/1/2013, $9,100 on 1/1/2014, $12,000 on 1/1/2015, and $5,500 on 1/1/2016. You are charged an annual interest rate, compounded annually, of 4% for each separate loan. You finally graduate from school in Spring 2016 and do not have to make your first payment until January 1, 2017; however, your loans accumulate interest charges beginning from the original date that you received each of the individual student loans. Assuming that you have not made any payments, how much will you owe the lender on January 1, 2017? You begin making payments on January 1, 2017, to pay back the loans. You pay off your loans by 2037, i.e. the last payment is made on January 1, 2037, with equal payments each year. What is the amount of your annualized payment? To obtain full credit for this problem your answer should include the following, a diagram showing cash flows, clearly written formulas for the appropriate time value of money factors that were used to solve the problem, and the computed monetary values as requested.

Explanation / Answer

P = PMT [(1 - (1 / (1 + r)n)) / r]

Where:

P = The present value of the annuity stream to be paid in the future

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are to be made

Calculate for each loan individually.

Years Cash Flow (P) NPER(n) Loan 1 1/1/13 $10,000 4 Loan 2 1/1/14 $9,100 3 Loan 3 1/1/15 $12,000 2 Loan 4 1/1/16 $5,500 1 Rate 4% Loan 1 Payment $2,754.90 Loan 2 Payment $3,279.17 Loan 3 Payment $6,362.35 Loan 4 Payment $5,720.00 Amount Owe to Lender NPER Loan 1 Payment $2,754.90 4 $11,019.60 Loan 2 Payment $3,279.17 3 $9,837.52 Loan 3 Payment $6,362.35 2 $12,724.71 Loan 4 Payment $5,720.00 1 $5,720.00 Total $39,301.82 Present Value(PV) $39,301.82 Nper 20 Rate 4% PMT (Annualized Payments) $2,891.90 Calculated in excel.

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