12. Your grandmother asks for your help in choosing a certificate of deposit (CD
ID: 2777039 • Letter: 1
Question
12. 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, #1 pays 2.95 percent APR compounded annually, while the second certificate of deposit, CD#2 pays 3.00 percent APR compounded monthly. What is the effective annual rate (the EAR ) of each CD and which CD do you recommend to your grandmother?
1. If the first certificate of deposit, #1 pays 2.95 percent APR compounded annually, the EAR for the deposit is ______% (Round to two decimal places.)
2. Based on the findings above, which CD do you recommend to your grandmother? (Select the best choice below)
a. CD #1 that pays 2.95% compounded annually
b. CD #2 that pays 3.00% compounded monthly
Explanation / Answer
Solution:
APR is the Annual Percentage Rate quoted by the issuer of the security, in this case certificate of deposit. It can be compounded annually, semiannually, quarterly or monthly. It is also known as nominal rate of interest.
EAR or Effective Annual Rate is the effective interest rate on a loan or security restated from APR or nominal rate with annual compound interest payable in arrears. Hence, it gives a proper comparison of all APR with different compounding periods.
EAR = (1+APR/n)n - 1 where n is the compounding period within one year
In the question CD1 pays 2.95% APR componded annually, hence n = 1,
so EAR = (1+2.95%/1)1 - 1
= 2.95%
For CD1, APR = 3%, n = 12, since compounding is monthly
Hence, EAR = (1+3%/12)12 - 1
= 1.002512 - 1
= 1.0304 - 1 = 0.0304
or EAR = 3.04%
so, EAR of CD1 = 2.95% and CD2 = 3.04%
Since CD2 pays more interest with annual compounding, grandmother should buy CD2
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