A student bought a $75 used guitar and agreed to pay for it with a single $80 payment at the end of 3 months. What is the nominal annual interest rate? What is the effective interest rate?

29.5%

Explanation:

Effective interest rate is the actual interest rate that a investor receives on invesment or a borrower pays on loan including the compounding effect.

APR = (80 - 75) / 75 = 0.067 = 6.67%

Effective interest rate = (1 + APR) ^n - 1

Effective interest rate = (1 + 6.67%) ^4 - 1

Effective interest rate = (1.0667) ^4 - 1

Effective interest rate = 1.2947 - 1

Effective interest rate = 0.2947

Effective interest rate = 29.5%