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