Assume an 18-month CD purchased for $7000 pays an APR of 3% compounded monthly. What is the APY?
To find the APY (Annual Percentage Yield), we need to use the formula:
APY = (1 + r/n)^n - 1
Where:
- r is the annual interest rate in decimal form,
- n is the number of compounding periods per year.
In this case, the annual interest rate is 3% (or 0.03 in decimal form), and since the CD is compounded monthly, the number of compounding periods per year is 12.
Now let's plug in these values into the formula and calculate the APY:
APY = (1 + 0.03/12)^12 - 1
First, let's evaluate the expression inside the parentheses:
(0.03 / 12) = 0.0025
(1 + 0.0025)^12 = 1.025
Now plug this value into the formula:
APY = 1.025 - 1
APY = 0.025
To express this as a percentage, multiply by 100:
APY = 0.025 * 100
APY = 2.5%
Therefore, the APY for the 18-month CD with an APR of 3% compounded monthly is 2.5%.