Question

You are considering an investment in a mutual fund with a 4% load and expense ratio of 0.5%. You can invest instead in a bank CD paying 6% interest. a. If you plan to invest for 2 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

Answer 1

It must earn an annual rate of return of 8.69%

Step-by-step explanation:

Mathematically;

(1+Rcd)^t = (1-front-end-load) * (1 + Rmutual fund - Expense ratio)^t

From the question;

Rcd = 6% = 6/100 = 0.06

t = 2 years

Front-end-load = 4% = 4/100 = 0.04

Expense ratio = 0.005

Rmutualfund = ? (let’s call it Rmf for convenience sake)

Substituting these values, we have;

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

1.06^2 = 0.96 * (Rmf + 0.995)^2

1.1236/0.96 = (Rmf + 0.995)^2

1.170417 = (0.995 + Rmf)^2

0.995 + Rmf = (1.170417)^1/2

Rmf = 1.0819-0.995

Rmf = 0.0869 = 8.69%