Bobby deposits $8000. Determine the APY if there is an APR of 7% compounded monthly. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
To calculate the APY (Annual Percentage Yield) when interest is compounded monthly, we can use the following formula:
APY = (1 + (APR/n))^n - 1
where APR is the annual percentage rate and n is the number of compounding periods per year.
In this case, APR = 7% and n = 12 since the interest is compounded monthly.
APY = (1 + (0.07/12))^12 - 1
APY = (1 + 0.005833)^12 - 1
APY = (1.005833)^12 - 1
APY = 1.071646 - 1
APY ≈ 0.071646
To convert this decimal to a percentage, we multiply by 100:
APY ≈ 7.1646%
Therefore, the APY of a deposit with an APR of 7% compounded monthly is approximately 7.16%.