Question

troy deposits $8000 . determine the apy if there is an apr of 5.5% compounded quartely. express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.

Answer 1

The APY, given an APR of 5.5% compounded quarterly, is calculated using the compound interest formula. Upon calculation, the APY is approximately 5.61% when rounded to the nearest hundredth of a percent.

Step-by-step explanation:

To determine the annual percentage yield (APY) for an annual percentage rate (APR) of 5.5% compounded quarterly, we use the formula for compound interest. The formula to convert APR to APY is APY = (1 + {r/n})n - 1, where r is the annual interest rate (as a decimal) and n is the number of compounding periods per year.

For Troy's deposit, the APR is 5.5% or 0.055 in decimal form, and since the interest is compounded quarterly, n equals 4. Plugging these values into the formula gives us:

APY = (1 + 0.055/4)4 - 1

APY = (1 + 0.01375)4 - 1

APY = 1.056136 - 1

APY ≈ 0.0561 or 5.61%

After rounding to the nearest hundredth of a percent, the APY is 5.61%.