Question

A student bought a $75 used guitar and agreed to pay for it with a single $79.30 payment at the end of 3 months. What is the (yearly) effective interest rate?

Answer 1

Lets first find the 3 month interest rate.

That i = (79.3 - 75)/75. So annual interest rate = 4i

Formula:

Effective annual interest rate = (1 + r/n)ⁿ - 1

where r = annual interest rate = 4i = 17.2/75 , n = number of compounded period in a year = 4 because here there is a time period of 3 months, so in a year it will be 12/3 = 4.

Hence using above details and formula we get:

Effective annual interest rate = (1 + (17.2/75)/4)⁴ - 1 = 0.2498 ~ 24.98%

Hence, Effective annual interest rate = 24.98% or 25% (approx)