Question

Your grandmother asks for your help in choosing a certificate of deposit​ (CD) from a bank with a​ one-year maturity and a fixed interest rate. The first certificate of​ deposit, CD​ #1, pays 1.95 percent APR compounded monthly​, while the second certificate of​ deposit, CD​ #2, pays 2.00 percent APR compounded weekly. What is the effective annual rate​ (the EAR) of each​ CD, and which CD do you recommend to your​ grandmother?

Answer 1

1.97% and 2.01%

Explanation:

The computation of the effective annual rate is shown below:-

Effective annual rate = (1 + Annual percentage rate ÷ n)^n -1

For CD 1

= (1 + 0.0195 ÷ 12)^12 - 1

= (1 + 0.001625 )^12 - 1

= (1.001625 )^12 - 1

= 1.97%

For CD 2

= (1 + 0.02 ÷ 2)^2 - 1

= (1 + 0.01 )^2 - 1

= (1.01)^2 - 1

= 2.01%

CD 2 will recommend to the grandmother