Your friend is celebrating her 50th birthday today and wants to start saving for her anticipated retirement at age 68. She wants to be able to withdraw $10,000 from her savings account each month for 20 years following her retirement; the first withdrawal will be made one month after retirement. Your friend intends to invest her money in the local credit union, which offers 6% interest per year. She wants to make equal monthly payments into the account established at the credit union for her retirement fund.

a. Suppose your friend has just inherited a large sum of money. Rather than making equal monthly payments, she has decided to make one lump-sum payment on her 50^th birthday to cover her retirement needs. What amount does she have to deposit?

b. Suppose your friends employer will contribute $200 to the account every month as part of the companys profit-sharing plan. In addition, your friend expects a $50,000 distribution from a family trust fund on her 60^th birthday, which she will also put into the retirement account. What amount must she deposit monthly now to be able to make the desired withdrawal at retirement?