Problem

What's the annual percentage yield for money invested at the rate of $4.8 \%$ compounded quarterly? Answer: Convert your answer into a percentage. Round your answer to 2 decimal places.

Solution

Step 1 :Given that the annual interest rate is 4.8%, which is 0.048 in decimal form, and the interest is compounded quarterly, which means 4 times a year. We are looking for the annual yield, so the time the money is invested for is 1 year.

Step 2 :Using the formula for APY, which is APY = \((1 + r/n)^{nt} - 1\), where r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 3 :Substitute the given values into the formula: APY = \((1 + 0.048/4)^{4*1} - 1\)

Step 4 :Calculate the result to get the annual percentage yield.

Step 5 :Final Answer: The annual percentage yield for money invested at the rate of 4.8% compounded quarterly is \(\boxed{4.89 \%}\)

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Source: https://solvelyapp.com/problems/33606/

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