Reference no: EM131964206

You are trying to choose between investing in an Index mutual fund (that mimics the S&P500) or buying units of an exchange-traded fund (ETF) that invests directly in the S&P500. Both investments give you exposure to the S&P500, but the difference is in the way fees are assessed. The mutual fund subtracts an annual fee of 2% from the gross returns on the portfolio. The S&P500 is expected to grow at a rate of 11% (0.9167% per month) in the future, so the return on the index mutual fund will be 9% (0.75% per month). You are 30 years old today. You plan to save $600 per month at the end of each month until your 60th birthday. So, you expect to accumulate $1,098,446.08 by investing in the mutual fund. Alternatively, you could invest in the ETF. With the ETF there are no management expenses which reduce the return- you will earn the same return as the S&P500. However, you pay a brokerage commission each time that you trade. How big does the trading commission ($fee) have to be on the ETF in order for the future value of the two strategies to be equal? (Assume monthly periodicity and monthly purchases of the ETF. Ignore any commission on selling at age 60)