At age 23​, someone sets up an IRA​ (individual retirement​ account) with an APR of 6​%. At the end of each month he deposits ​$55 in the account. How much will the IRA contain when he retires at age​ 65?  Compare that amount to the total deposits made over the time period. 
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Part 1
After retirement the IRA will contain ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
Part 2
The total deposits made over the time period is ​$
  
enter your response here. 
​(Type a whole​ number.)

This problem involves a future value calculation for an annuity (specifically, a series of monthly deposits). We will use the future value formula for an ordinary annuity, where payments are made at the end of each period.

### Part 1: Future Value Calculation

The formula for the future value of an ordinary annuity is:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $ FV $ is the future value.
- $ P $ is the regular monthly deposit ($55).
- $ r $ is the monthly interest rate (APR of 6% means $ 6\%/12 = 0.005 $ per month).
- $ n $ is the total number of deposits (from age 23 to 65, so $ 65 - 23 = 42 $ years, or $ 42 \times 12 = 504 $ months).

Let's plug in the values:

- $ P = 55 $
- $ r = 0.005 $
- $ n = 504 $

### Part 2: Total Deposits Made

The total deposits made over the time period can be calculated as:

\[
\text{Total Deposits} = P \times n
\]

Now, let me calculate the results for both parts.### Part 1: Future Value of the IRA
The IRA will contain approximately **$124,858.81** when the individual retires at age 65.

### Part 2: Total Deposits Made
The total amount deposited over the period is **$27,720**.

Would you like any more details or have any other questions?

Here are 5 related questions to consider:
1. How would the future value change with a higher interest rate?
2. What if the monthly deposit was increased to $100?
3. How does starting earlier (e.g., at age 20) impact the final amount?
4. What if the deposits were made at the beginning of each month instead of the end?
5. How much would be saved if the interest rate were compounded daily instead of monthly?

**Tip:** The earlier you start investing, even with smaller amounts, the more you benefit from compound interest over time.

At age 23, someone sets up an IRA (individual retirement account) with an APR of 6%. At the end of each month he deposits $55 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.

Discover how to calculate the future value of an IRA with monthly deposits of $55 at an APR of 6%. Learn the step-by-step process, including the future value of an annuity formula, and compare the final amount with total deposits over 42 years. Suitable for high school students learning finance or algebra.

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