Your local bank just loaned you $1,501. This amount is net of a 10% discount on the loan proceeds, which serves as interest on the loan. You are to repay the loan in one year. What is the effective rate at which you borrowed?

Question

Quizplus · Accepted Answer

The effective rate can be calculated by dividing the interest amount by the actual loan proceeds. The interest amount is the difference between the face value of the loan and the net proceeds. If $1,501 is net of a 10% discount, the face value of the loan is $1,501 / (1 - 0.10) = $1,501 / 0.90 = $1,667.78. The interest is $1,667.78 - $1,501 = $166.78. Therefore, the effective rate is $166.78 / $1,501 = 11.11%.

Your Local Bank Just Loaned You $1,501