Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $105,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers a quoted rate of 7 percent interest per year, compounded semi-annually. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

(a) If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

(b) (b) Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit?

(c) Your friend decides not to use her inheritance in part (b) for her retirement. Instead, your friend tells you her employer has announced they will contribute $1,500 to her retirement account every year as part of the company's profit-sharing plan. These contributions will start at the end of the current year (i.e. your friend will receive her first contribution on her 36th birthday), and will continue until she retires at age 65. In addition, your friend expects a $150,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually to be able to make the desired withdrawals at retirement?