Question

For a recent 10-year period, a mutual fund company reported performance (average annual
return) for two of its funds as follows:
Fund Average Return
Equity-Income Fund 10.50 percent
Personal Strategy Growth Fund 9.50 percent
Assume you invested $10,000 in each fund at the beginning of this 10-year period.
(a) How much difference would there be in the ending wealth (after 10 years) between the
two funds?
(b) For the same two funds, the ending wealth after five years was $1.45 per dollar invested
for the Equity-Income Fund and $1.25 per dollar invested for the Personal Strategy
Growth Fund. What were that annual average returns for each fund for this five-year
period?

Answer 1

a).

If 10000 was invested in Equity income fund, ending wealth after 10 years will be

P*(1+r)^n

= 10000*(1+10.5%)^10

= 10000*2.714081

= 27140.81

If 10000 was invested in Personal strategy growth fund, ending wealth after 10 years would be

P*(1+r)^n

= 10000*(1+9.5%)^10

= 10000*2.478228

= 24782.28

So, Difference in ending wealths is 27140.81-24782.28= $2358.53

b).

For equity income fund, given that

ending wealth after 5 years is $1.45 for dollar invested. Average annual return can be calculated using the formula: ((Ending Investment/Initial Investment)^(1/n))-1

On substituting, we get

((1.45/1)^(1/5))-1

= 1.0771-1

= 7.71%

So, annual average return for equity income fund is 7.71%

For personal strategy growth fund, given that

ending wealth after 5 years is $1.25 for dollar invested.

So, using the above formula, we get,

((1.25/1)^(1/5))-1

= 1.0456-1

= 4.56%

So, annual average return for personal strategy growth fund is 4.56%