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To save for retirement, you decide to deposit $100 at the end of each month in an IRA that pays 5.5% compounded monthly. How much will you have from the IRA 30 years? Find the interest?

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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.

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