This section contains problem 7 out of 7 problems. The problem is worth 10 points. Show your work for each problem for credit. Ignore transaction costs and taxes for the problems. Please fit all your work for the problems on one side of the paper, write your name on the sheet, make a digital file of the sheet, and upload the file. Assume all returns are annual returns unless otherwise indicated. 7. Your friend is celebrating her 25 th birthday today and wants to start saving for her anticipated retirement at age 65 . She wants to be able to withdraw \\( \\$ 400,000 \\) from her saving account on each birthday for 25 years following her retirement; the first withdrawal will be on her 66 th birthday. Your friend intends to invest her money in a retirement account, which earns 8 percent return per year. She wants to make an equal annual deposit on each birthday into the account for her retirement fund. Assume that the annual return on the retirement account is 8 percent before retirement and 6 percent after retirement. If she starts making these deposits on her 26th birthday and continue to make deposits until she is 65 (the last deposit will be on her 65 th birthday and the total number of annual deposits is 40), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Hint: One way to solve for this problem is to first find the value on your friend's 65 th birthday of the \\( \\$ 400,000 \\) withdrawal per year for 25 years after her retirement using the annual return after retirement and then find the equal annual deposit that she needs to make from her 26th birthday to 65 th birthday using the annual return before retirement.) Ignore taxes and transaction costs for the