Problem $5-41$ Retirement Savings $($LO$3)$

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. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Annual savings

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? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Annual savings