Final answer:
The effective annual yield on Sofia's investment, which is compounded semiannually at a 7% interest rate, is slightly more than 7%. After applying the effective annual yield formula, the answer is calculated to be 7.1225%, rounding to the nearest option gives us 7.25%.
Step-by-step explanation:
The question pertains to the concept of the effective annual yield on an investment where the interest is compounded semiannually. To find the effective annual yield, we use the formula for compound interest and account for the frequency of compounding within the year. For an interest rate of 7% compounded semiannually, the effective annual yield (EAY) can be calculated using the formula:
EAY = (1 + r/n)n - 1
where r is the annual nominal rate (0.07 for 7%), and n is the number of compounding periods per year (2 for semiannually). Plugging these values in, we get:
EAY = (1 + 0.07/2)2 - 1
EAY = (1 + 0.035)2 - 1
EAY = 1.0352 - 1
EAY = 1.071225 - 1
EAY = 0.071225 or 7.1225%
The answer is slightly more than 7% due to compounding effect. Therefore, the correct choice is (B) 7.25%.