It is reported that an annuity$-$immediate with $$100$ annual payments for s years has an accumulated value of $$933\mathrm{.}52$ at the time of its last payment. Further more, an annuity$-$immediate that has $$40$ annual payments and a term four times as long accumulates to $$2,680\mathrm{.}11$ at the time of its last payment. Now consider an annuity that has the same term as the second of these annuities but $$2,400$ and each further payment is $$300$ more than its predecessor. Express the accumulated value of this third annuity at the time of its last payment as a function of the annual effective interest rate i$.$ Make sure any annuity symbols appearing in the function are to be evaluated at the rate i used in valuing the first two annuities.