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?
Sophie's situation can be modeled using the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the amount of money in Sophie's account after t years
P = the initial amount of money Sophie deposited (in this case $3500)
e = the base of the natural logarithm (approximately 2.71828)
r = the interest rate (in decimal form, in this case 0.0705)
t = the number of years
Using this formula, we can calculate the amount of money in Sophie's account after 3 years and 10 years.
For 3 years:
A = 3500 * e^(0.0705 * 3)
A ≈ 3500 * e^(0.2115)
A ≈ 3500 * 1.2356
A ≈ $4323.60
After 3 years, there will be approximately $4323.60 in Sophie's account.
For 10 years:
A = 3500 * e^(0.0705 * 10)
A ≈ 3500 * e^(0.705)
A ≈ 3500 * 2.0247
A ≈ $7096.45
After 10 years, there will be approximately $7096.45 in Sophie's account.