While in college Ellen recieved 40000 in student loans at 8

While in college, Ellen recieved $40,000 in student loans at 8% interest. She will graduate in June and is expected to begin repaying the loans in either 5 or 10 equal payments. Computer her yearly payments for both repayment plans.

Solution

1) Loan payment in 5 annual payments

Amount Borrowed = $40000

Interest rate (r) = 8% = 8/100 = 0.08

Time (t) = 5

Annual Payment = Amount Borrowed * r* (1+r)^t / (1+r)^t - 1

                           = 40000 * 0.08 (1+0.08)⁵ / (1+0.08)⁵ - 1

                           = 40000 * 0.08 * 1.469328 / 1.469328 - 1

                           = 40000 * 0.117546 / 0.469328

                           = 4701.85 / 0.469328

                           = $10018.26

So the 5 equal payment to repay the $40000 loan is $10018.26

2) Loan Payment in 10 annual payments

Amount Borrowed = $40000

Interest rate (r) = 8% = 8/100 = 0.08

Time (t) = 10

Annual Payment = Amount Borrowed * r* (1+r)^t / (1+r)^t - 1

                           = 40000 * 0.08 (1+0.08)¹⁰ / (1+0.08)¹⁰ - 1

                           = 40000 * 0.08 * 2.158925 / 2.158925 - 1

                           = 40000 * 0.172714 / 1.158925

                           = 6908.56 / 1.158925

                           = $5961.18

So the 10 equal payment to repay the $40000 loan is $5961.18