A couple will retire in $50$ years; they plan to spend about $$32,000$ a year $($in current dollars$)$ in retirement, which should last about $25$ years. They believe that they can earn a real interest rate of $9\%$ on retirement savings.

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.

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

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?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.