Question

Banks sometimes quote interest rates in the form of “add-on interest.” In this case, if a 1-year loan is quoted with an interest rate of 8.5% and you borrow $1,000, then you pay back $1,164. But you make these payments in monthly installments of $97 each.

a. What is the true APR on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. What is the effective annual rate on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

a. Amount borrowed = 1000, Monthly payments = $97, Period of loan = 1 year = 12 months

We know that APR = 12 x monthly rate

To find the APR of this loan we will first need to find monthly rate of this loan,

We can find the monthly rate using rate function in excel

Formula to be used in excel: =rate(nper,-pmt,pv)

Using rate function in excel, we get monthly rate = 2.4173%

APR = monthly rate x 12 = 2.4173% x 12 = 29.0076 = 29.01% (rounded to two decimal places)

b.

Effective annual rate for loan = (1 + monthly rate)^{no of months in a year} - 1 = (1 + 2.4173%)¹² - 1 = (1.024173)¹² - 1 = 1.331925 - 1 = 0.331925 = 33.1925% = 33.19% (rounded to two decimal places)