Final answer:
To calculate the future value of monthly deposits in an IRA with a 5.5% interest rate compounded monthly over 30 years, use the future value of an annuity formula. After finding the future value, subtract the total deposits to find the interest earned.
Step-by-step explanation:
To determine how much you would have after depositing $100 at the end of each month for 30 years into an IRA with a 5.5% annual interest rate, compounded monthly, we can use the future value of an annuity formula. The formula is as follows:
FV = P * [((1 + r)^n - 1) / r]
Where:
- FV is the future value of the annuity.
- P is the payment amount per period ($100 in this case).
- r is the interest rate per period (5.5% annual rate compounded monthly means 0.055 / 12 per month).
- n is the total number of payments (360 payments over 30 years).
Using this formula, we can calculate:
FV = 100 * [((1 + 0.055/12)^(12*30) - 1) / (0.055/12)]
After doing the calculations, this will give us the total amount in the IRA after 30 years. To find the interest earned, subtract the total of the deposits ($100 * 12 * 30) from the future value obtained. This compound interest effect is a powerful tool for growing wealth over time, as demonstrated in the provided examples.