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%
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.
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