Question

Jamal and Demetrius are both 25 and plan to invest $5000 each year for the next 40 years for retirement. Jamal plans to invest in the Vanguard Total U.S. Stock Market Fund which he thinks has a "gross" expected annualized return of 8.00%. However, its "net" expense ratio is 7.95% as Vanguard charges a 0.05% expense ratio. Demetrius, by contrast, has chosen an actively-managed fund which also has a "gross" expected annualized return of 8.00%. However, the XYZ Corporation that runs the fund charges a typical 0.75% annual expense ratio so the "net" expected return is 7.25%. How much more is Jamal "expected" to have after 40 years of investing than Demetrius?

Answer 1

Investment amount = $5000 per year

Investment period = 40 years

Net expected return for Jamal = 7.95%

Net expected return for Demetrius = 7.25%

Assuming the investment is made at the end of each year

Future value of investments can be calculated using FV function in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = net expected return

number of periods = 40 years

payment amount = yearly investment = $5000

present value = present value of investments = 0

when-due = when is the investment made each year = end = 0

Future value of Jamal's investments = FV(7.95%, 40, -5000, 0, 0) = $1,278,353.85

Future value of Demetrius' investments = FV(7.25%, 40, -5000, 0, 0) = $1,064,802.06

Difference = $1,278,353.85 - $1,064,802.06 = $213,551.80

Hence Jamal is expected to have $213,551.80 more than Demetrius after 40 years of investing