An individual earns an extra $2000 each year and places this money at the end of each year into an Individual Retirement Account (IRA) in which both the original earnings and the interest in the account are not subject to taxation. If the account has an annual interest rate of 10.2% compounded annually, how much is in the account at the end of 40 years? (Round your answer to the nearest cent.)

To solve this problem, we use the **future value of an ordinary annuity formula**, which is applied when regular payments (in this case, annual contributions) are made into an account that earns compound interest. The formula is as follows:

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

Where:
- $A$ is the future value of the annuity (the total amount in the account at the end of the investment period),
- $P$ is the payment made at the end of each period (annual contribution),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the number of periods (years).

### Given:
- $P = 2000$ (annual contribution),
- $r = 10.2\% = 0.102$,
- $t = 40$ years.

Now, let's calculate the future value of the account.

\[
A = 2000 \times \frac{(1 + 0.102)^{40} - 1}{0.102}
\]

I'll compute this.The amount in the account at the end of 40 years will be approximately **$934,711.23**.

Would you like any additional details or have any questions?

Here are 5 related questions to explore:
1. How much interest is earned on the principal over the 40 years?
2. What happens if the interest rate changes to 8%?
3. How much will be in the account after 30 years instead of 40 years?
4. What if the contribution increases to $3000 annually?
5. How does compounding semi-annually affect the final amount?

**Tip**: Regular contributions with compound interest can lead to significant growth due to the effects of interest compounding over time.

An individual earns an extra $2000 each year and places this money at the end of each year into an Individual Retirement Account (IRA) in which both the original earnings and the interest in the account are not subject to taxation. If the account has an annual interest rate of 10.2% compounded annually, how much is in the account at the end of 40 years? (Round your answer to the nearest cent.)

Discover how to calculate the future value of an Individual Retirement Account (IRA) with an annual contribution of $2000 and an interest rate of 10.2% compounded annually over 40 years. This solution explores the annuity formula for compound interest, ideal for students in Grades 11-12.

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