A couple will retire in $40$ years; they plan to spend $$21,848\mathrm{.}45$ a year $($in current dollars$)$ in

retirement, which should last about $20$ years. They believe that they can earn a real interest rate

of $6\%$ 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 one year.