What is the present value of $400 invested each year for 12 years at a rate of 6%?

Multiple Choice

$814

$2,861

$3,354

$6,748

$9,586

To calculate the present value (PV) of $400 invested each year for 12 years at a 6% interest rate, we can use the formula for the present value of an ordinary annuity:

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

Where:
- $ P = 400 $ (the annual investment),
- $ r = 0.06 $ (the annual interest rate),
- $ n = 12 $ (the number of years).

Now, let's calculate this step by step:

\[
PV = 400 \times \frac{1 - (1 + 0.06)^{-12}}{0.06}
\]The present value of $400 invested each year for 12 years at a 6% interest rate is approximately **$3,354**. Therefore, the correct answer is:

\[
\boxed{3,354}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How does the present value change if the interest rate is 8% instead of 6%?
2. What is the future value of this investment after 12 years at 6%?
3. How does compounding frequency affect the present value in this scenario?
4. How would the result differ if the payments were made at the beginning of each year (annuity due)?
5. What if the investment period was extended to 15 years at the same interest rate?

**Tip:** The present value of an annuity decreases as the interest rate increases, because future payments are discounted more heavily.

What is the present value of $400 invested each year for 12 years at a rate of 6%?

Calculate the present value of $400 invested annually for 12 years at a 6% interest rate using the formula for the present value of an ordinary annuity. This problem helps students understand key financial concepts such as interest rates, time value of money, and annuities. Suitable for Grades 10-12.

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