Question

1. Compare the expenses on two mutual funds that follow the same index: S&P 500. The first fund is PEOPX (Dreyfus S&P 500 Index) and it's expense ratio is 0.5% per year. The second fund is VFIAX (Vanguard S&P 500 Index) with an expense ratio of 0.05% per year.

2. Assume that both funds will return 10% per year until YOUR retirement (you will have your own number of years here) and that you will invest $5,500 per year starting today all the way until you retire.

please calculate mutual fund fees and compare which mutual fund is better to invest.

3. Calculate the difference in future values for PEOPX and VFIAX at your retirement age (Hint: subtract the annual expense ratio from the annual return and use the difference to compute future value of your contributions).

4. Find a comparable item (an iPhone, a TV set, a car (which model?) etc.) that most closely represents this difference.

Answer 1

Answer:

1. Mutual Fund Fees:

For PEOPX = 5500*0.5%=$27.5

For VFIAX=5500*0.05%=$2.75

2. Comparision and Suggestion:

As the Investment in both the mutual funds is same and both the funds yield same rate of return with same maturity Period, the Mutual fund expenses with VFIAX is Lower and it is better to invest in VFIAX.

3. Future values of Mutual Fund PEOPX and VFIAX:

Future Value for Annuity =P((1+r)ⁿ-1)/r

Where,

P=Principle Amount or Amount of Investment every year

r= rate of Interest

n=number of years(Assumed Funds will retire after 10 years)

Rate of Interest=Rate of return-Expense Ratio

Rate of Intrest for PEOPX is 10%-0.5%=9.5%

Rate of Intrest for VFIAX is 10%-0.05%=9.95%

Future Value for PEOPX = 5500((1+0.095)¹⁰ -1)/0.095

=5500(2.4782-1)/0.095

=5500(1.4782)/0.095

=$85580

Future Value for VFIAX = 5500((1+0.0995)¹⁰-1)/0.0995

=5500(2.5820-1)/0.0995

=5500(1.5820)/0.0995

=$87447

The difference between two future values of PEOPX and VFIAX is $85580-$87447= $1867.

4. As the difference is around $1867, The difference can be eqivalent to Samsung - 55" Class (55" Diag.) - LED - 2160p - Smart - 4K Ultra HD TV .