Roy deposits $7000. Determine the APY if there is an APR of 6.5% compounded quartely. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
To find the APY, we need to first find the effective annual rate (EAR) using the formula:
EAR = (1 + (APR/n))^n - 1
Where:
APR = annual percentage rate = 6.5% = 0.065
n = number of compounding periods per year = 4 (quarterly compounding)
EAR = (1 + (0.065/4))^4 - 1
EAR = (1 + 0.01625)^4 - 1
EAR = (1.01625)^4 - 1
EAR = 1.066358 - 1
EAR = 0.066358
Now, to find the APY, we need to convert the EAR to a percentage:
APY = EAR * 100
APY = 0.066358 * 100
APY = 6.64%
Therefore, Roy's deposit has an APY of 6.64% when there is an APR of 6.5% compounded quarterly.