Final answer:
To save $32,000 in four years with a 5.5% annual interest rate compounded monthly, Jane must calculate the monthly deposit required using the future value of an annuity formula, considering the future value, the interest rate, and the number of deposits.
Step-by-step explanation:
Jane wants to accumulate $32,000 by saving money each month for the next four years in a savings account that pays a 5.5% annual interest rate, compounded monthly. This type of problem is best solved using the future value of an annuity formula, which in this case can be written as:
FV = P × { [(1 + r)³⁶⁴ − 1] ÷ r }
Where:
- FV is the future value of the annuity, which is $32,000 in this scenario.
- P is the monthly payment or deposit.
- r is the monthly interest rate, which is the annual interest rate divided by 12.
- n is the total number of deposits (4 years × 12 months).
Substituting the given values into the formula, we need to solve for P as follows:
$32,000 = P × { [(1 + 0.055/12)³⁶⁴ − 1] ÷ (0.055/12) }
Calculating this will give us the monthly deposit amount Jane needs to make to reach her goal of $32,000 in four years.