Large jackpots in most U$.$S$.$ lotteries are paid out in equal annual installments. The winner can also

request immediate payment, but in this case the jackpot is reduced and only the so$-$called "cash

value" is paid out. For the sake of simplicity, we will ignore the fact that lottery winnings are

considered taxable income in the United States. For example, in Connecticut, large jackpots are

paid out in $21$ equal installments $($with the first installment payable immediately when the winner

is confirmed$)$ and the cash value is $57\%$ of the total jackpot. So$,$ if you happened to win $$1,000,000$

on Connecticut Lotto, you would receive $$1,000,\frac{000}{21}=$$$47,619\mathrm{.}05$ right now, another

$$47,619\mathrm{.}05$ one year from now etc. until all $21$ installments have been paid. Alternatively, you could

tell the Lotto administrator that you want to receive the cash value of $$1,000,0000\mathrm{.}57=$$$570,000$

right now. Below you will find the number of annual installments and the cash value of two popular

U$.$S$.$ lotteries:

Suppose that the annual interest rate $($EAR$)$ is $8\%,$ would you choose the installments or the cash value

if you won a million dollar on the Connecticut Lotto? How about the Michigan $-$ Classic Lotto $47?$

What is the difference $($in terms of present value$)$ between the annual installments and the cash values

of the two lotteries? $(5$ points$)$