How to calculate the effective interest rate of a loan that must be paid back with interest as lump sum
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 ,400 today, if you agree to
repay a lump sum of ,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 00 in interest over four years amounts to 0 per year, which is 17% of 00. I believe the correct answer should be 17%.
Am I wrong? and why?
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If you were actually paying 0/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 00 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 00 yields the ending amount of 00. Hint: Your calculations will need to include calculating the fourth root of some number.
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