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 weekly, while the second certificate of deposit, CD #2, pays 6.00 percent APR compounded monthly. What is the effective annual rate (the EAR) of each CD, and which CD do you recommend to your grandmother? If the first certificate of deposit, CD #1, pays 5.95 percent APR compounded weekly, the EAR for the deposit is%. (Round to two decimal places.)

Answer 1

To find the effective annual rate (EAR) of each CD, use the formula for compound interest. CD #1 has a slightly higher EAR than CD #2.

Step-by-step explanation:

To find the effective annual rate (EAR) of each certificate of deposit (CD), we can use the formula for compound interest:

EAR = (1 + r/n)^n - 1

Where:

• r is the annual interest rate
• n is the number of compounding periods in a year

For CD #1 with 5.95% APR compounded weekly, the EAR can be calculated as:

EAR = (1 + 0.0595/52)^52 - 1 = 0.061714...

For CD #2 with 6.00% APR compounded monthly, the EAR can be calculated as:

EAR = (1 + 0.06/12)^12 - 1 = 0.061678...

Comparing the EARs, CD #1 has a slightly higher effective annual rate of 6.17%, while CD #2 has an effective annual rate of 6.17%. Therefore, I would recommend CD #1 to your grandmother.