You are on the board of a local non$-$profit that will provide a $$5,000$ grant every $6$ months to

local elementary schools to help fund enrichment activities like music and art. These

semiannual grants will continue indefinitely. You will award the first grant on July $1,2024,$ the

second of January $1,2025,$ the third on July $1,2025,$ and so on$.$ The investment account in

which you will deposit and keep your funds earns $4\mathrm{.}10\%$ compounded annually $($that is$,$ an

effective annual rate of $4\mathrm{.}10\%).$

$16.$ Assume first that today is January $1,2024,$ so your first grant is awarded in $6$ months. How

much would your non$-$profit need to deposit today to fund the grants indefinitely?