Question

You are considering an investment in a mutual fund with a 4% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 6% 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

Answer 1

a. r > 8.69%

b. r > 7.225

Step-by-step explanation:

Missing question "b. hat annual rate of return must the fund portfolio earn if you plan to invest for 6 years to be better off in the fund than in the CD?"

Mutual fund wealth index after N years = (1 - front load)*(1+r-expenses)^N

CD wealth index after N years = (1+rate)^N

a. Investment for 2 years

(1 - front load)*(1+r-expenses)^N = (1+rate)^N

(1 - 0.04)*(1+r-0.005)^2 = (1+0.06)^2

0.96*(1+r-0.005)^2 = 1.1236

(1+r-0.005)^2 = 1.17041667

We remove square from both sides

(1+r-0.005) = 1.17041667^(1/5)

(1+r-0.005) = 1.08185797

r = 1.08185797 - 1 + 0.005

r = 0.0869

r = 8.69%

r > 8.69%

b. If investment is for 6 years

(1 - front load)*(1+r-expenses)^N = (1+rate)^N

(1 - 0.04)*(1+r-0.005)^6 = (1+0.06)^6

0.96*(1+r-0.005)^6 = 1.41851911

(1+r-0.005)^6 = 1.47762408

We remove square from both sides

(1+r-0.005) = 1.47762408^(1/6)

(1+r-0.005) = 1.06723648

r = 1.06723648 - 1 + 0.005

r = 0.07223648

r = 7.22%

r > 7.225