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An example question asks:

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?

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If you were actually paying $400/year in interest, then your 17% would be a closer approximation of the correct answer of 16 2/3 % in such a case.

However, that case is not matching the question. Interest is not being paid each year. Rather, the interest is accumulating into the debt until you owe $4000 total at the end of the four years.

Consequently, you need to determine the effective annual interest rate; i.e. the rate that when compounded four times and applied to the starting amount of $2400 yields the ending amount of $4000. Hint: Your calculations will need to include calculating the fourth root of some number.

  • Thank you for your explanation. If the question was modified to be over a 20 year time span, I would need to find a 20th root? Is there a better way? – CodyBugstein Feb 28 '16 at 23:42
  • @Imray Yes, in that case you would need to find the 20th root, or equivalent, raise the number to the 1/20th power. Here's a video at Khan Academy that explains the relationship between radicals and unit-fraction exponents. – Chris W. Rea Feb 29 '16 at 0:23
  • 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
  • I suggest you search Khan Academy for additional videos about interest rates and compounding. – Chris W. Rea Feb 29 '16 at 0:28
  • Do you know if there's a quick way to solve this on a financial calculator? – CodyBugstein Feb 29 '16 at 4:11

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