Answer with hand writing on paper, please.

$(24$ points$)$ An alumni association wants to establish a scholarship fund that can provide $$500,000$ annually for scholarships for $20$ years, starting exactly $6$ years from now $($i$.$e$.,$ starting $t=6).$ The association is planning to make the following cash contributions$-$ an initial contribution now $)$ followed by $5$ annual through $t=5)$ contributions. The association just contributed $$750,000.$ If the fund is expected to earn $15\%$ per year compounded annually, determine the annual contribution the association would have to make over the next $5$ years.