Question

You are considering three alternative investments:

A three-year bank CD paying 7.52 percent compounded quarterly. Calculate effective annual interest rate (EAR)? (Round answer to 2 decimal places, e.g. 15.25%.)

Effective Annual Rate: %

A three-year bank CD paying 7.32 percent compounded monthly. Calculate effective annual interest rate (EAR)? (Round answer to 2 decimal places, e.g. 15.25%.)

Effective Annual Rate: %

A three-year bank CD paying 7.82 percent compounded annually. Calculate effective annual interest rate (EAR)? (Round answer to 2 decimal places, e.g. 15.25%.)

Effective Annual Rate: %

Which of the above investments has the highest effective annual interest rate (EAR)?

a. 7.52%

b. 7.82%

c. 7.32%

Answer 1

Alternative 1:

Annual Interest Rate, APR = 7.52%
Number of compounding per year, n = 4

Effective Annual Rate = (1 + APR/n)^n - 1
Effective Annual Rate = (1 + 0.0752/4)^4 - 1
Effective Annual Rate = 1.0188^4 - 1
Effective Annual Rate = 1.0773 - 1
Effective Annual Rate = 0.0773 or 7.73%

Alternative 2:

Annual Interest Rate, APR = 7.32%
Number of compounding per year, n = 12

Effective Annual Rate = (1 + APR/n)^n - 1
Effective Annual Rate = (1 + 0.0732/12)^12 - 1
Effective Annual Rate = 1.0061^12 - 1
Effective Annual Rate = 1.0757 - 1
Effective Annual Rate = 0.0757 or 7.57%

Alternative 3:

Annual Interest Rate, APR = 7.82%
Number of compounding per year, n = 1

Effective Annual Rate = (1 + APR/n)^n - 1
Effective Annual Rate = (1 + 0.0782/1)^1 - 1
Effective Annual Rate = 1.0782^1 - 1
Effective Annual Rate = 1.0782 - 1
Effective Annual Rate = 0.0782 or 7.82%

Alternative 3 has the highest EAR.