Final answer:
The student's question is about calculating the future value of an annuity with monthly deposits and compound interest. The monthly interest rate must be used along with the number of total payments to apply the future value of an annuity formula. This formula will provide the total amount in the account after 20 years.
Step-by-step explanation:
The student's question involves calculating the future value of an annuity with regular deposits and compound interest. Since the interest rate given is an annual rate but the compounding is monthly, we need to adjust the interest rate to a monthly one, which would be ∆ = 2.75% / 12 months = 0.22916% per month (or 0.0022917 as a decimal).
To find the total amount in the savings account after 20 years, we can use the future value of an annuity formula:
FV = P × [ ((1 + r)⁾ˆⁿ - 1 ] / r ]
Where FV is the future value of the annuity, P is the payment amount per period, r is the monthly interest rate as a decimal, and n is the total number of payments. In this case, P is $500, r is 0.0022917, and n is 20 years times 12 months/year = 240 months.
Plugging these values into the equation gives us the future value of the annuity. We need to calculate and add the future value of each $500 monthly deposit, using the formula for the future value of an individual payment, and sum these up over the 240 payments.