A couple will retire in 40 years; they plan to spend about $37,000 a year in retirement, which should last about 20 years. They believe that they can earn 7% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year.

b. How would the answer to part (a) change if the couple also realize that in 15 years they will need to spend $67,000 on their childs college education?