Question

A loan shark lends money on the following term: "If I give you $100 on Monday, you owe me $115 on the following Monday."

(A) What nominal interest rate per year (r) is the loan shark charging?

Answer 1

The loan shark is charging a nominal interest rate of 7.8% per year.

Step-by-step explanation:

To determine the nominal interest rate per year, we need to find the rate at which the loan amount of $100 increases to $115 in one week. The increase in the amount is $15, which is the interest charged. We can calculate the interest rate per week by dividing the interest amount by the principal amount: $15/$100 = 0.15. To convert this weekly rate to an annual rate, we multiply it by 52 (the number of weeks in a year): 0.15 x 52 = 7.8. Therefore, the loan shark is charging a nominal interest rate of 7.8% per year.