Rhett deposits $7000. Determine the APY if there is an APR of 8% compounded monthly. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
To determine the APY when the APR is 8% compounded monthly, we use the formula for compound interest:
APY = (1 + (APR/n))^n - 1
Where:
APR = Annual Percentage Rate (8% in this case)
n = number of times interest is compounded per year (12 for monthly compounding)
Plugging in the values:
APY = (1 + (0.08/12))^12 - 1
APY = (1 + 0.00666667)^12 - 1
APY = (1.00666667)^12 - 1
APY = 1.08384072 - 1
APY = 0.08384072
To express this as a percentage, we multiply by 100:
APY = 8.38%
Therefore, the APY when Rhett deposits $7000 with an APR of 8% compounded monthly is 8.38%.