A couple will retire in 50 years; they plan to spend about $32,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% 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 20 years they will need to spend $62,000 on their child's college education?