What is the effective annual rate on a certificate of deposit that promises to pay interest at a 6.6 percent rate, compounded monthly?
To calculate the effective annual rate (EAR) on a certificate of deposit (CD) that compounds interest monthly, you can use the following formula:
EAR = (1 + (nominal interest rate / number of compounding periods)) ^ (number of compounding periods) - 1
In this case, the nominal interest rate is 6.6 percent, and the CD compounds interest monthly. Since there are 12 months in a year, the number of compounding periods is 12.
Let's plug in the values into the formula:
EAR = (1 + (0.066 / 12)) ^ 12 - 1
First, divide the nominal interest rate by the number of compounding periods:
0.066 / 12 = 0.0055
Then, add 1 to the result:
1 + 0.0055 = 1.0055
Next, raise this sum to the power of the number of compounding periods:
1.0055 ^ 12 ≈ 1.06744
Finally, subtract 1 from the result:
1.06744 - 1 = 0.06744
Therefore, the effective annual rate on the certificate of deposit is approximately 6.744 percent.