cole starts an IRA at the age of 26, he deposits $400 every month. when he is 65, the account has $1,474,258.37 in it. how much money did he deposit and what was the intrest

### Step 1: Calculate the Total Deposits
Cole deposits $400 every month from the age of 26 to 65.

- **Number of years**: 65 - 26 = 39 years
- **Number of months in 39 years**: 39 × 12 = 468 months
- **Total deposits**: 468 months × $400 = **$187,200**

### Step 2: Interest Earned
The final value of the IRA account when Cole is 65 is $1,474,258.37, and he deposited a total of $187,200.

- **Interest earned**: Final amount - Total deposits
- **Interest earned** = $1,474,258.37 - $187,200 = **$1,287,058.37**

### Step 3: Estimate the Interest Rate (Using the Future Value of an Annuity Formula)
We can estimate the average annual interest rate $ r $ using the future value of an annuity formula:

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

Where:
- $ FV $ is the future value of the investment ($1,474,258.37),
- $ P $ is the monthly deposit ($400),
- $ r $ is the monthly interest rate (unknown),
- $ n $ is the number of months (468).

To find $ r $, we'd need to solve the equation numerically, which can be done using software or financial calculators. However, based on the data provided, the interest rate is likely to be in the range of 7% to 8% annually (a typical estimate for long-term investments like IRAs).

Would you like me to calculate the exact interest rate for you?

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### Additional Questions:
1. What happens if Cole starts saving earlier or later?
2. How would increasing or decreasing the monthly deposit impact the final amount?
3. What is the impact of a different interest rate, say 5% or 10%, on the final balance?
4. How does compound interest work in long-term investments like an IRA?
5. What would the total be if Cole continued to deposit for 5 more years?

### Tip:
Always start saving early, even small amounts, to maximize the power of compound interest over time!

Cole starts an IRA at the age of 26, he deposits $400 every month. When he is 65, the account has $1,474,258.37 in it. How much money did he deposit and what was the interest?

Learn how to calculate the total amount deposited and the interest earned in an IRA account where $400 is deposited monthly for 39 years. The final balance is $1,474,258.37. Understand key financial formulas, including compound interest and the future value of an annuity. Suitable for high school and college-level students.

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