Question

Problem 6.32 a-d You are considering three alternative investments: A three-year bank CD paying 7.32 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 7.12 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 7.62 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)? The three-year bank CD paying has the highest effective yield. Click if you would like to Show Work for this question:

Answer 1

Quarterly compounded:
Formula: 1(1+ r/4)^n*4 - 1
1(1 + 0.0732/4)^3*4 -1 = 1(1.0183)^12 - 1 = 1.24311 - 1 = 0.24311
Effective Annual Interest Rate = 0.24311/3 = 0.0810 or 8.10%
Monthly compounded:
Formula: 1(1+ r/12)^n*12 - 1
1(1 + 0.0712/12)^3*12 -1 = 1(1.00593333)^36 - 1 = 1.237346 - 1 = 0.237346
Effective Annual Interest Rate = 0.237346/3 = 0.0791 or 7.91%
Annually compounded:
Formula: 1(1+ r)^n - 1
1(1 + 0.0762)^3 -1 = 1(1.0762)^3 - 1 = 1.246462 - 1 = 0.246462
Effective Annual Interest Rate = 0.246462/3 = 0.0822 or 8.22%
Of the three EAI rates, the annually compounded EAI rate is the highest.