A so-called friend has offered to loan you $1,000 for one year. At the end of the year you must pay your friend $2,000. What is the APR on this loan if interest is compounded daily?

Question

Quizplus · Accepted Answer

The APR can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,000), r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, A = $2,000, P = $1,000, n = 365 (since interest is compounded daily), and t = 1 year. Rearranging the formula to solve for r gives us the APR. Plugging the numbers into the formula and solving for r gives an APR of approximately 69.38%.

A So-Called Friend Has Offered to Loan You $1,000 for One