1. 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?
   
   
   
   
2. 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?
   
   
   
   
3. 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?