You see on TV that the Mega Millions is up to $2 million! You decide to buy a ticket ......... and you WIN!!! Unfortunately, you do not get that amount right away. Instead, this is the future value of an annuity. Let us examine some choices you have regarding your big win. a) You could choose to collect your winnings today, in the present day. The lottery people could invest this present value and earn 2.7% interest, compounded annually, and have the $2 million in 25 years. How much would they give you today? b) The interest rate in part (a) is very conservative. You have a “friend” who advises you to take the money today and invest it with him, at 6.6% compounded quarterly, for those 25 years. How much would you have in 25 years if you did this? (What is the future value of the amount you computed in part (a)?) c) Otherwise, you could choose to take the annuity. They will pay you nothing in the present day but will pay you A dollars each month for 25 years. Assume 2.7% interest compounded monthly, and that the future value is $2 million, as advertised. How much will you get each month? (It may help to think of this as if you are investing a certain amount each month in order to earn a specific future value, just like in a sinking fund.)
You see on TV that the Mega Millions is up to $2 million! You decide to buy a ticket .........
and you WIN!!! Unfortunately, you do not get that amount right away. Instead, this is the
a) You could choose to collect your winnings today, in the present day. The lottery people could
invest this present value and earn 2.7% interest, compounded annually, and have the $2
million in 25 years. How much would they give you today?
b) The interest rate in part (a) is very conservative. You have a “friend” who advises you to take
the money today and invest it with him, at 6.6% compounded quarterly, for those 25 years.
How much would you have in 25 years if you did this?
(What is the future value of the amount you computed in part (a)?)
c) Otherwise, you could choose to take the annuity. They will pay you nothing in the present day
but will pay you A dollars each month for 25 years. Assume 2.7% interest compounded
monthly, and that the future value is $2 million, as advertised.
How much will you get each month?
(It may help to think of this as if you are investing a certain amount each month in order to earn
a specific future value, just like in a sinking fund.)
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