In: Finance
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?
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%