# How to calculate the effective interest rate of a loan that must be paid back with interest as lump sum

Student Bank has agreed to lend you funds to complete the last year of your degree. The bank will lend you \$2,400 today, if you agree to repay a lump sum of \$4,000 in 4 years from now. What is the approximate annual rate of interest that Student Bank is charging you?

The solution given in the textbook here says that the answer is 14%. However, I've calculated that \$1600 in interest over four years amounts to \$400 per year, which is 17% of \$2400. I believe the correct answer should be 17%.

Am I wrong? and why?

• Aside from using root/power, you can get closer to the right answer through approximation. e.g. by guessing the interest rate and appyling it 4 times (or 20 times, in the modified case). e.g. try 1.12: `2400*1.12*1.12*1.12*1.12=3776.45` ... so 1.12 is too low, try higher; 1.14: `2400*1.14*1.14*1.14*1.14=4053.50` ... too high; a bit lower, etc. – Chris W. Rea Feb 29 '16 at 0:26