For your retirement "nest egg," you deposit $400 at the end of each month into a bank account paying 5% interest compounded monthly. Find the amount of this annuity at the end of your 40-year working career. 

To find the amount of the annuity at the end of a 40-year working career, we can use the formula for the future value of an ordinary annuity (since the deposits are made at the end of each month):

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the regular monthly deposit ($400).
- $r$ is the monthly interest rate (5% annually, so $\frac{5\%}{12} = \frac{0.05}{12} = 0.004167$).
- $n$ is the total number of payments (40 years × 12 months = 480 payments).

Now, let's plug in the values:

\[
FV = 400 \times \frac{(1 + 0.004167)^{480} - 1}{0.004167}
\]

We can now calculate this step-by-step.

1. $1 + 0.004167 = 1.004167$
2. $1.004167^{480} \approx 7.10696$
3. $7.10696 - 1 = 6.10696$
4. $\frac{6.10696}{0.004167} \approx 1465.38$
5. $FV = 400 \times 1465.38 \approx 586,152$

So, the future value of the annuity at the end of your 40-year career would be approximately **$586,152**.

Would you like a detailed breakdown or have any questions?

Here are 5 related questions to expand on this topic:
1. How does the future value change if the interest rate is increased to 6%?
2. What happens if the deposits are made at the beginning of each month instead of the end?
3. How does the total amount change if you deposit $500 per month instead of $400?
4. What is the effect of a shorter 30-year career on the future value?
5. How would inflation impact the real value of the retirement savings?

**Tip:** The higher the frequency of compounding, the more interest you earn on your investment.

For your retirement "nest egg," you deposit $400 at the end of each month into a bank account paying 5% interest compounded monthly. Find the amount of this annuity at the end of your 40-year working career.

Learn how to calculate the future value of a retirement annuity where $400 is deposited at the end of each month into a bank account with 5% interest compounded monthly. This detailed step-by-step solution covers key concepts such as compound interest and the future value of annuities, suitable for Grades 10-12.

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