DO YOU EVEN ALGEBRA 2?

Question

Ed has just declared you the winner in the Grand Publisher’s Sweepstakes. You have a choice of two prizes:

Receive $150,000 in one lump sum.
OR

Receive a super savings bond called Better Bond that has an initial value of $1 but doubles in value every year until it matures in 20 years. Hint: When the money “matures,” it can be cashed in.
Which of the two prizes would you select? Please explain your reasoning.

Answer 1

Looking at both options, Option A of taking the lump sum of $150,000 will cause our earnings to just be $150,000. Looking at Option B now, we can see that the money has an initial value and will double the money every year from the previous year. So writing out an equation for that we get the Total = P * (2^t), where P is the initial amount and 2^t is representative of the money doubling, an exponential growth function where t represents the total number of years. Using what we were given of the initial value of $1 which doubles every year for 20 years, means that we get a new equation of Total = (1) * (2^20) which yields $1,048,576. Option B of receiving a total of $1,048,576 after 20 years seems more favorable than Option A where simply a one time payment of $150,000 is received.