QuestionJune 15, 2025

At age 20, someone sets up an IRA (individual retirement account) with an APR of 7% At the end of each month he deposits 50 in the account. How much will the IRA contain when he retires at age 65?Compare that amount to the total deposits made over the time period. After retirement the IRA will contain square (Do not round until the final answer. Then round to the nearest cent as needed.)

At age 20, someone sets up an IRA (individual retirement account) with an APR of 7% At the end of each month he deposits 50 in the account. How much will the IRA contain when he retires at age 65?Compare that amount to the total deposits made over the time period. After retirement the IRA will contain square (Do not round until the final answer. Then round to the nearest cent as needed.)
At age 20, someone sets up an IRA (individual retirement account) with an APR of 7%  At the end of each month he deposits 50 in the account. How much will the
IRA contain when he retires at age 65?Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain square 
(Do not round until the final answer. Then round to the nearest cent as needed.)

Solution
4.7(230 votes)

Answer

After retirement, the IRA will contain approximately \348,845.70. Explanation 1. Calculate the number of deposits The person deposits monthly from age 20 to 65, which is 45 years. Total deposits = 45 \times 12 = 540. 2. Calculate total deposits Total deposits = 540 \times 50 = \27,000. 3. Use future value formula for annuities The future value of an ordinary annuity is given by **FV = P \frac{(1 + r)^n - 1}{r}**, where P = 50, r = \frac{0.07}{12}, and n = 540. 4. Substitute values into the formula FV = 50 \frac{(1 + \frac{0.07}{12})^{540} - 1}{\frac{0.07}{12}}. 5. Calculate the future value FV = 50 \frac{(1.0058333)^{540} - 1}{0.0058333}. 6. Compute using a calculator FV \approx 50 \times 348.8457 \approx \17,442.29.

Explanation

1. Calculate the number of deposits<br /> The person deposits monthly from age 20 to 65, which is $45$ years. Total deposits = $45 \times 12 = 540$.<br /><br />2. Calculate total deposits<br /> Total deposits = $540 \times 50 = \$27,000$.<br /><br />3. Use future value formula for annuities<br /> The future value of an ordinary annuity is given by **$FV = P \frac{(1 + r)^n - 1}{r}$**, where $P = 50$, $r = \frac{0.07}{12}$, and $n = 540$.<br /><br />4. Substitute values into the formula<br /> $FV = 50 \frac{(1 + \frac{0.07}{12})^{540} - 1}{\frac{0.07}{12}}$.<br /><br />5. Calculate the future value<br /> $FV = 50 \frac{(1.0058333)^{540} - 1}{0.0058333}$.<br /><br />6. Compute using a calculator<br /> $FV \approx 50 \times 348.8457 \approx \$17,442.29$.
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