Final answer:
The future value of an IRA with monthly deposits of $50 at a 5% annual interest rate compounded monthly for 35 years is $20,222.20.
Step-by-step explanation:
To calculate how much you would have in an IRA at retirement, we can use the future value of an annuity formula since you are making regular monthly deposits. The formula for the future value of an annuity compounded monthly is:
FV = P * [((1 + r/n)^(nt) - 1) / (r/n)]
Where:
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- P is the monthly deposit
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- r is the annual interest rate (expressed as a decimal)
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- n is the number of times the interest is compounded per year
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- t is the number of years the money is invested
Let's plug in your numbers:
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- P = $50
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- r = 0.05
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- n = 12 (monthly compounding)
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- t = 65 - 30 = 35 years
Thus, the future value of your annuity at retirement would be:
FV = 50 * [((1 + 0.05/12)^(12*35) - 1) / (0.05/12)]
By calculating this, we see the future value of your annuity at retirement is:
FV = $50 * [((1 + 0.0041667)^(420) - 1) / 0.0041667]
FV = $50 * [(2.68558 - 1) / 0.0041667]
FV = $50 * [404.444]
FV = $20,222.20
Your IRA would have $20,222.20 when you retire at 65, given a 5% return compounded monthly with $50 contributions every month for 35 years.