Reconsider the situation described in Problem 4. Assume that rather than annual deposits, she makes monthly deposits. The first deposit will be 1 month from today, and the last deposit will be 40 years from today. Assume that the stock market return is 10.4 percent per year compounded monthly.

Data from problem 4

A 22-year-old engineering graduate wants to accumulate \(\$ 2,000,000\) to be available when she retires 40 years from today. She investigates several investment options and decides to invest in a stock market index fund after discovering that the long-term average return for the stock market is 10.4 percent per year. Since this will be a tax sheltered account, she plans to ignore the impact of taxes.

a. If she plans to make uniform monthly deposits, what is the dollar amount of the monthly deposit?

b. If she earns a 4 percent annual raise each year throughout her career (starting 1 year from today) and adjusts her monthly deposits by the same 4 percent each year, how much will be in the account immediately after the last deposit?