This is a classic retirement problem. A time line will help solving it. Your friend is celebrating her 36^th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $87,000 from her savings account on each birthday for 13 years following her retirement; the first withdrawal will be on her 66^th birthday. Your friend intends to invest her money in the local credit union, which offers 8 percent interest per year. She wants to make equal 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 next birthday (a year from now) and continues to make deposits on each birthday until she is 65 (the last deposit will be on her 65^th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Round to the nearest cent) $

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 36^th birthday to cover her retirement needs. What amount does she have to deposit? (Round to the nearest cent) $