Math Word Problem

Question

Suppose you borrowed a certain amount of money 318 weeks ago at an annual interest rate of 3.6% with semiannual compounding (2 times per year). If you returned $11156 today, how much did you borrow?

Round your answer to the nearest dollar. 

Answer 1

You borrowed about $8,974.43 318 weeks ago.

Since this is a problem requiring compounded interest, then we can use the formula A = P(1 + (r/n))^nt, where is A is the future amount, P is the current amount, r is the annual rate, n is the number of compounds per year, and t is time in years. Since it is compounded semiannually at a rate of 3.6% and 318 weeks from the borrow you are paying $11,156, A = 11156, r = 0.036, n = 2, and t = (318)(7) / 365. After plugging these values in, we get:

11156 = P(1 + (0.036)/2)^{(2)((318)(7) / 365)}

P ≈ 8,974.43

Therefore, you borrowed $8,974.43 318 weeks ago.