Question

Suppose you pay back $575 on a $525 loan you had for 75 days. What was your simple annual interest rate? State your result to the nearest hundredth of a percent.

Answer 1

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

What is the interest rate behind a pay back?

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

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