Investment A offers a 9% return compounded semiannually, and investment B offers a 8.81% return compounded continuously. Which investment has a higher rate of return over a 4-yr period?

Question

Investment A offers a 9% return compounded semiannually, and investment B offers a 8.81% return compounded continuously. Which investment has a higher rate of return over a 4-yr period? ​

Quizplus · Accepted Answer

To compare the two investments, we need to calculate their respective effective annual rates.

For Investment A, the semiannual interest rate is 4.5% (9% / 2) and the number of compounding periods in 4 years is 8 (2 semiannual periods per year for 4 years). Using the formula for effective annual rate, we have:

EAR_A = (1 + (0.045))^8 - 1 = 9.22%

For Investment B, the continuous interest rate is 8.81%. Using the formula for continuous compounding, we have:

EAR_B = e^(0.0881) - 1 = 9.15%

Therefore, Investment B has a higher effective annual rate and offers a higher rate of return over a 4-year period.

Investment a Offers a 9% Return Compounded Semiannually, and Investment