Final answer:
To calculate the future value of monthly deposits with compound interest, the future value of an annuity formula is used. By plugging in the periodic deposit, interest rate, and number of deposits into the formula, you can determine the amount the deposits will grow to over time.
Step-by-step explanation:
To find the future value of regular monthly deposits with compound interest, you can use the future value of an annuity formula:
FV = P × { [ (1 + r)^n - 1 ] / r }
Where:
- FV is the future value of the annuity.
- P is the periodic deposit amount.
- r is the monthly interest rate (annual rate divided by 12).
- n is the total number of deposits (years multiplied by 12).
In this scenario, the student deposits $69.00 every month for 7.75 years, with an annual interest rate of 11% compounded monthly. First, convert the interest rate to a monthly rate by dividing by 12. Then, calculate n, which is the number of months in 7.75 years. Using the formula:
P = $69.00
r = 0.11/12
n = 7.75 × 12
Substitute these values into the formula to find the future value (FV) of the deposits.