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 2: Describe the type of equation that models Jack’s situation. Create that equation of Jack’s situation. Using the equation you created, how much money will be in Jack’s account after 3 years? 10 years?
Jack's situation can be modeled using the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount in the account
P = the initial amount (given as $3520)
r = interest rate (6.5% or 0.065 as a decimal)
n = number of times interest is compounded per year (for annually, n = 1)
t = number of years
Plugging in the values:
A = 3520(1 + 0.065/1)^(1*t)
After simplifying, the equation becomes:
A = 3520(1 + 0.065)^t
To calculate how much money will be in Jack's account after 3 years, substitute t = 3:
A = 3520(1 + 0.065)^3
A ≈ $4,032.54
To calculate how much money will be in Jack's account after 10 years, substitute t = 10:
A = 3520(1 + 0.065)^10
A ≈ $6,946.48