Final answer:
To determine the total amount in an IRA after 30 years with $100 monthly deposits at a 5.5% annual interest rate compounded monthly, use the future value of an annuity formula. The formula incorporates the deposit amount, periodic interest rate, and total number of payments to calculate the future value of the annuity.
Step-by-step explanation:
To calculate how much you will have in your IRA after 30 years with a monthly deposit of $100 and an annual interest rate of 5.5% compounded monthly, we should use the future value of an annuity formula. The formula for the future value of an annuity is:
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
Where:
FV is the future value of the annuity.
For this situation, P is $100, r is 0.055/12 (since it's compounded monthly), and n is 30 \times 12 (for 30 years of monthly contributions).
Applying these values into the formula, calculate the future value:
FV = $100 \times \left(\frac{(1 + 0.055/12)^{30 \times 12} - 1}{0.055/12}\right)
After calculating the above, you would arrive at the total amount you would have after 30 years. This calculation assumes that the 5.5% interest rate remains constant over the entire 30 years and all payments are made regularly at the end of each month.