An agent is selling an investment that earns 4.875% compounded semiannually. What is the APY (in percent) of the investment? (Round your answer to the nearest hundredth of a percent.)

Question

show your work

Answer 1

To find the APY (Annual Percentage Yield) of the investment, we can use the formula:

APY = (1 + (r/n))^n - 1

where:
r = annual interest rate
n = number of compounding periods per year

Given:
Annual interest rate (r) = 4.875%
Number of compounding periods per year (n) = 2 (semiannual)

Convert the annual interest rate to a decimal:
r = 4.875% = 0.04875

Now plug the values into the formula:

APY = (1 + 0.04875/2)^2 - 1
APY = (1 + 0.024375)^2 - 1
APY = (1.024375)^2 - 1
APY = 1.049394 - 1
APY = 0.049394

Convert the APY back to a percentage:
APY = 0.049394 * 100% = 4.94%

Therefore, the APY of the investment is 4.94%.