Question

You are considering an investment in a mutual fund with a 5% load and an expense ratio of 0.7%. You can invest instead in a bank CD paying 7% interest. a. If you plan to invest for two years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % b. If you plan to invest for six years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 0.95% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return %

Answer 1

1. Annual Rate of Return

(1 + Bank Return)^2 = (1 - Front End Load) * (1 + Mutual Fund Return - Expense ration)^2

(1 + 0.07)^2 = (1 - 0.05) * (1 + Mutual Fund Return - 0.007)^2

1.1449 = 0.95 * (0.993 + Mutual Fund Return)^2

(0.993 + Mutual Fund Return)^2 = 1.205157

0.993 + Mutual Fund Return = 1.0977

Mutual Fund Return = 10.48%

Annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD is 10.48%

2.  Annual Rate of return for six Years

(1 + Bank Return)^6 = (1 - Front End Load) * (1 + Mutual Fund Return - Expense ration)^6

(1 + 0.07)^6 = (1 - 0.05) * (1 + Mutual Fund Return - 0.007)^6

1.5007 = 0.95 * (0.993 + Mutual Fund Return)^6

(0.993 + Mutual Fund Return)^2 = 1.579716

0.993 + Mutual Fund Return = 1.079186

Mutual Fund Return = 8.62%

Annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD is 8.62%

The Annual Rate of return is changed because of increase in time value

3. Annual Rate of return with 12b-1 for 2 years

(1 + Bank Return)^2 = (1 + Mutual Fund Return - 12b-1 Fees - Expense ratio)^2

(1 + 0.07)^2 = (1 + Mutual Fund Return - 0.0095 - 0.007)^2

1.1449 = (0.9835 + Mutual Fund Return)^2

(0.9835 + Mutual Fund Return)^2 = 1.1449

0.9835 + Mutual Fund Return = 1.07

Mutual Fund Return = 8.65%

Annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD is 8.65%

Annual Rate of return with 12b-1 for 6 years

(1 + Bank Return)^6 = (1 + Mutual Fund Return - 12b-1 Fees - Expense ratio)^6

(1 + 0.07)^6 = (1 + Mutual Fund Return - 0.0095 - 0.007)^6

1.07 = (0.9835 + Mutual Fund Return)

(0.9835 + Mutual Fund Return) = 1.07

0.9835 + Mutual Fund Return = 1.07

Mutual Fund Return = 8.65%

Annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD is 8.65%