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 40 uniform annual deposits starting 1 year from today, what is the dollar amount of the required deposits?

b. If she makes the first of the 40 deposits starting today rather than 1 year from today, what is the dollar amount of the required deposits?

c. If she plans to make the first payment 1 year from today and each annual payment will be \(\$ 200\) greater than the previous year's payment,

(i) what is the dollar amount of the first deposit?

(ii) what is the dollar amount of the last deposit?

d. If she plans to make the first payment 1 year from today and each annual payment will be 5 percent greater than the previous year's payment,

(i) what is the dollar amount of the first deposit?

(ii) what is the dollar amount of the last deposit?