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?
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?
The problem is asking for a description of the equation that represents Jack's situation, and then using that equation to calculate the amount of money in Jack's account after 3 years and 10 years.
We know that Jack was given $3520 and he decides to put it in an account with a 6.5% interest rate that is compounded annually.
To calculate the amount of money in Jack's account after a certain number of years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = $3520, r = 6.5%, n = 1 (compounded annually), and we need to calculate A for 3 years and 10 years.
The equation that models Jack's situation is therefore: A = 3520(1 + 0.065/1)^(1*3) for 3 years, and A = 3520(1 + 0.065/1)^(1*10) for 10 years.