Question

Gunther decides Central Perk needs a refresh. He was just thinking of repainting, but Phoebe and Monica convinced him to buy new couches and tiny tables so customers can relax and use the Wi-Fi. Gunther’s bank offers to lend Gunther $10,000 for one year at a nominal annual rate of 19.50%, but he must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

a. 19.71%

b. 15.94%

c. 22.02%

d. 20.97%

e. 17.62%

Answer 1

Nominal rate = 19.50%
Compounding periods = 4 (since interests are paid quarterly)

Effective annual rate = (1 + Nominal rate/Compounding period)^ Compounding period -1

= (1 +19.5%/4)^4 -1

= 20.97%

Correct choice D