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 5.95 percent APR compounded quarterly​, while the second certificate of​ deposit, CD​ #2, pays 6.00 percent APR compounded annually. What is the effective annual rate​ (the EAR) of each​ CD, and which CD do you recommend to your​ grandmother?

If the first certificate of​ deposit, CD​ #1, pays 5.95 percent APR compounded quarterly​, the EAR for the deposit is ______%​(Round to two decimal​ places.)

Answer 1

Effective Annual Rate is calculated as follows

i=(1+r/n)n−1

r= Rate of Interest

n= number of periods

CD#1 5.95% APR compounded quarterly

n= 12/3 =4

EAR= (1+5.95%/4)^4-1

EAR=(1+0.014875) ^4-1

EAR= 1.060841-1

EAR= 6.08%

CD#2 6.0% APR compounded annually

As EAR IS higher for CD#1 it is recommended

If the first certificate of​ deposit, CD​ #1, pays 5.95 percent APR compounded quarterly​, the EAR for the deposit is 6.08%