Question

SU2020 Saved A local finance company quotes a 13 percent interest rate on one-year loans. So, if you borrow $30,000, the interest for the year will be $3,900. Because you must repay a total of $33,900 in one year, the finance company requires you to pay $33,900/12, or $2,825.00 per month over the next 12 months. a. What rate would legally have to be quoted? b. What is the effective annual rate? < Prev 17 of 40 *

Answer 1

a]

Legally, the APR has to be quoted.

APR is calculated using RATE function in Excel :

nper = 12 (total number of monthly payments)

pmt = -2825 (Monthly payment. This is entered with a negative sign because it is a cash outflow)

pv = 30000 (Amount borrowed. This is entered with a positive sign because it is a cash inflow today)

The rate calculated is the monthly APR. To get annual APR, we multiply by 12.

APR is 23.19%

A6 x =RATE(12,-2825,30000)*12 B C D E F A 23.19% 6 LO

The rate to quote legally is 23.19%

b]

Effective annual rate (EAR) = (1 + (APR/n))ⁿ - 1

where n = number of compounding periods per year

EAR = (1 + (23.19%/12))¹² - 1

EAR = 25.82%