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?

To solve this, we need to determine two things:
1. **How much money did Cole deposit into the IRA?**
2. **What was the interest earned?**

### 1. Total amount deposited:
Cole started depositing at age 26 and continued until age 65, so he deposited for $65 - 26 = 39$ years.

He deposits $400 every month, so the total number of deposits is:
\[
39 \text{ years} \times 12 \text{ months/year} = 468 \text{ months}.
\]
Now, the total amount deposited is:
\[
\text{Total deposits} = 400 \text{ dollars/month} \times 468 \text{ months} = 187,200 \text{ dollars}.
\]

### 2. Interest earned:
The total amount in the account at age 65 is $1,474,258.37. The interest earned is the difference between the final amount and the total amount deposited:
\[
\text{Interest earned} = 1,474,258.37 - 187,200 = 1,287,058.37 \text{ dollars}.
\]

### Summary:
- **Total money deposited**: $187,200
- **Interest earned**: $1,287,058.37

Would you like to see a breakdown of how interest might have compounded over time or explore other scenarios?

#### Related Questions:
1. What was the average annual interest rate required for this growth?
2. How would the outcome change if the monthly deposit was higher?
3. What would the final balance be if Cole deposited for a shorter or longer period?
4. How much would the final balance change with different interest compounding frequencies (e.g., monthly vs. annually)?
5. How would inflation affect the value of the future $1,474,258.37 in today's dollars?

**Tip:** The power of compound interest can significantly boost savings over time, especially in long-term investments like an IRA.

Learn how to calculate the total deposits and interest earned in an IRA when making $400 monthly deposits from age 26 to 65, with a final balance of $1,474,258.37. This problem covers arithmetic and compound interest concepts suitable for Grades 10-12.

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