 A Powerball lottery from usatoday.com.
said
"For the jackpot worth 295 million, if there is one winner, then they
will have a choice between 25 annual payments of 11.8 million each
(Note that 25*11.8 =295) or a single lump sum payment of 170 million".
How can we compare the logical benefits of each choice?
Let's cut off the "million" to make it easier to work with (if you look
at the formulas for lump sum and periodic payment, this is ok to do, since it
is multiplication outside the parenthesis).
Setup Let's assume that if we took the
lump sum then we would leave the 170 in an account at 5% compounded
annually for the 25 years.
Setup Let's assume that if we took the annual payment then we would deposit each 11.8 annual payment into the same type of account
at 5% compounded annually for the 25 years.
Which yields more money? Which would you choose? Why?
At a higher interest rate, you can make more money yourself via lump
sum. At a lower rate, you can't earn a lot from lump sum, so it is
better to take periodic payments. At what rate would the earnings
be equal?
 Setup
How much do we need to invest now to have 100,000 in 63 years at
6.5% compounded monthly?
Setup
What if we will deposit a certain amount per month at 6.5% compounded
monthly instead?
How much must we put in per month to obtain 100,000 in 63 years?
Setup The problem with this scheme
is that we will be making payments for the next 63 years!
Instead, let's say we can afford a monthly payment of $20 at 6.5% compounded
monthly. How long will
it take for the money to grow to 100,000?

Setup
How long does it take to triple a lump sum of $1000 at 6% compounded yearly?
Setup How long does it take to triple a lump sum of $1000 at 6%
compounded monthly?
Setup
When can we get our $22,000 car if we can't get a car loan but are
forced to save up $200 a month into a 6% compounded monthly account?