Question

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​ 3: Describe the type of equation that models​ Sophie’s situation. Create that equation of​ Sophie’s situation. Using the equation you​ created, how much money will be in​ Sophie’s account after 3​ years? 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?

Answer 1

The problem is asking for the equation that models Sophie's situation and to calculate the amount of money in her account after 3 years and 10 years.

To create the equation, we need to use the formula for compound interest that is compounded continuously:

A = P*e^(rt)

Where:
A = the final amount of money in Sophie's account
P = Sophie's initial investment
r = the interest rate (in decimal form)
t = the time in years
e = Euler's number, approximately 2.71828

In Sophie's case, P = $3500 and r = 7.05% = 0.0705.

After 3 years, t = 3:
A = 3500*e^(0.0705*3)

After 10 years, t = 10:
A = 3500*e^(0.0705*10)