Derek receives a perpetuity. It has annual payments with the $$rst payment in

exactly eight years. The $$rst payment is $$10,000,$ the second is $$15,000,$ and

then the payments alternate between $$10,000$ and $$15,000$ until there have

been a total of thirty payments. After that, the payments are all $$10,000.$ Find

the present value of this perpetuity if i D $4\%$

answer is $32\mathrm{.}12891$