You are going to invest in a stock mutual fund with a front-end load of 6.5 percent and an expense ratio of 1.37 percent. You also can invest in a money market mutual fund with a return of 2.7 percent and an expense ratio of 0.20 percent. If you plan to keep your investment for 2 years, what annual return must the stock mutual fund earn to exceed an investment in the money market fund? What if your investment horizon is 8 years?

Kindly check explanation

Explanation:

Given the following :

Stock Mutual fund :

Front-end load (f) = 6.5% = 0.065

Expense ratio (e) = 1.37 % 0.0137

Money market Mutual fund :

Return (r) = 2.7% = 0.027

Expense ratio (e) = 0.002

Period of investment = 2 years

what annual return must the stock mutual fund earn to exceed an investment in the money market fund?

Money market = stock

(1 + r - e)^2 = (1 - f) (1 + r - e)^2

(1 + 0.027 - 0.002)^2 = (1 - 0.065)(1 + r - 0.0137)^2

1.050625 = 0.935(r + 0.9863)^2

Divide through by 0.935

1.050625 / 0.935 = (r + 0.9863)^2

Take Square root of both sides

1.0600 = r + 0.9863

1.0600 - 0.9863 = r

0.0737 = r

r = 0.0737 * 100%

r = 7.37%

2.) If investment horizon is 8 years

Money market = stock

(1 + r - e)^8 = (1 - f) (1 + r - e)^8

(1 + 0.027 - 0.002)^8 = (1 - 0.065)(1 + r - 0.0137)^8

1.21840 = 0.935(r + 0.9863)^8

Divide through by 0.935

1.21840 / 0.935 = (r + 0.9863)^8

1.303101 = (r + 0.9863)^8

Take 8th root of both sides

1.03365 = r + 0.9863

1.03365 - 0.9863 = r

0.04735 = r

r = 0.04735 * 100%

r = 4.74%