You deposit $1000 into a savings plan at the end of each year for thirty years. The interest rate per year compounded annually. Find the value of the annuity after 30 years

To calculate the value of an annuity after 30 years, where you deposit $1000 at the end of each year and the interest is compounded annually, we can use the formula for the future value of an ordinary annuity:

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

Where:
- $A$ is the future value of the annuity (what we are calculating).
- $P$ is the annual deposit (\$1000).
- $r$ is the annual interest rate (expressed as a decimal).
- $n$ is the number of years (30 years in this case).

We don't have the interest rate ($r$) in the question, so I'll show the general formula and you can plug in the interest rate. Let's use the formula step-by-step.

1. Plug in $P = 1000$, $n = 30$.
2. Enter your interest rate for $r$, and then calculate the future value using the formula.

If you have a specific interest rate in mind, feel free to provide it, and I can calculate the exact value for you.

Would you like to provide an interest rate or ask about anything else?

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Here are 5 related questions you might find useful:

1. What if you deposited at the beginning of each year?
2. How does the future value change if the interest rate compounds more frequently (monthly or quarterly)?
3. What if the deposit amount increases each year instead of staying constant?
4. How does inflation affect the real value of the annuity?
5. Can you compare this with a simple savings account that doesn't have compounding?

**Tip:** The power of compounding grows significantly with time, so long-term annuities can benefit greatly from higher interest rates!

You deposit $1000 into a savings plan at the end of each year for thirty years. The interest rate per year compounded annually. Find the value of the annuity after 30 years.

Learn how to calculate the future value of an annuity where $1000 is deposited annually for 30 years with compound interest. This problem covers key concepts like compound interest and the time value of money, using the formula A = P × ((1 + r)^n - 1) / r. Suitable for high school and college students.

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