Question

You are considering an investment of $10,000 in a mutual fund with a 2% front load and an annual expense ratio of 0.5%. You are also considering an investment in a bank CD paying 2% interest per year. Assuming risk is constant across the two investments, if you plan to invest for four years, what annual rate of return must the mutual fund earn for you to be better off in the mutual fund than in the bank CD

Answer 1

r > 3.02%

Step-by-step explanation:

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

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

If investment is 4 years

(1+0.02)*(1+r-0.005)^4 = (1+0.02)^4

0.98*(1+r-0.005)^4 = 1.08243216

(1+r-0.005)^4 = 1.08243216/0.98

(1+r-0.005)^4 = 1.10452261

Taking 4th root both side

(1+r-0.005) = 1.10452261^(1/4)

1 + r - 0.005 = 1.02516472

r = 1.02516472 - 1 + 0.005

r = 0.03016472

r = 3.02%, r > 3.02%