Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously.
Part 1: Describe the type of equation that models Jerry's situation. Create that equation of Jerry's situation. Using the equation you created, how much money will be in Jerry's account after 3 years? After 10 years?
Understand: In my own words, what is being asked in the problem and what does that mean?
Think: What do I know and what does it mean? What plan am I going to try?
In this problem, we are asked to describe the type of equation that models Jerry's savings situation. We are also asked to create that equation and determine how much money Jerry will have in his account after 3 years and after 10 years.
Jerry decides to start with $125 in his shoebox savings and saves an additional $50 every month. Therefore, we can represent Jerry's savings using a linear equation.
The equation that models Jerry's savings over time is:
S = 125 + 50t
where S is the total amount in Jerry's savings after t months.
To determine how much money Jerry will have in his account after 3 years (36 months), we substitute t = 36 into the equation:
S = 125 + 50(36)
S = 125 + 1800
S = 1925
Therefore, Jerry will have $1925 in his account after 3 years.
To determine how much money Jerry will have in his account after 10 years (120 months), we substitute t = 120 into the equation:
S = 125 + 50(120)
S = 125 + 6000
S = 6125
Therefore, Jerry will have $6125 in his account after 10 years.