Assume an 18-month CD purchased for $7000 pays an APR of 7% compounded monthly. What is the APY?
(Fill in the blank below and round your answer to 2 decimal places.)
APY = %
To calculate the APY (Annual Percentage Yield), we need to convert the APR (Annual Percentage Rate) to an annualized rate that accounts for compounding.
The formula for APY is:
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 APR is 7% and it is compounded monthly, so the annual interest rate (r) is 7% or 0.07, and the number of compounding periods (n) is 12 (monthly).
To calculate the APY:
APY = (1 + 0.07/12)^12 - 1
= (1.00583)^12 - 1
≈ 0.0716
Therefore, the APY is approximately 7.16%.
P = Po(1+r)^n.
r = (7%/12)/100% = 0.005833 = Monthly % rate expressed as a decimal.
n = 12Comp/yr. * 1.5yrs. = 18 Compounding periods.
P = 7000(1.005833)^18 = $7737.90.
APY = ((P-Po)/Po)*100 =