Question

Alex invests his money in an account paying 2% interest compounded semiannually. What is the effective annual yield on this account? Enter your response as a percentage rounded to two decimal places and omit the percent sign (7.25% should be input as 7.25.)

Answer 1

Answer: 2.01%.

Step-by-step explanation:

Suppose Alex invests $1 into the account for one year. The formula is A=P0⋅(1+rk)N⋅k with P0=$1. We know that r=0.02 and k=2 compounding periods per year. Now, N=1 year. Substituting the values we have A=$1⋅(1+0.022)2=$1.0201. Now, to calculate the effective annual yield, we will use the formula rEFF=A−P0P0. rEFF=1.0201−11=0.0201 or 2.01%. When rounded to two decimals, rEFF=2.01%. However, do not include the % in your answer.