What is the future value of $400 invested each year for 15 years at a rate of 6%?

Multiple Choice

$959

$6,000

$9,310

$12,310

$14,959

To calculate the future value of an investment where regular annual payments are made, we can use the formula for the **future value of an annuity**:

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

Where:
- $ P $ is the payment made each year ($400),
- $ r $ is the interest rate per period (6% or 0.06),
- $ n $ is the number of periods (15 years).

Now, applying the values:

\[
FV = 400 \times \frac{(1 + 0.06)^{15} - 1}{0.06}
\]

Let's calculate this step-by-step.

First, calculate $ (1 + 0.06)^{15} $:

\[
(1.06)^{15} = 2.396558
\]

Now, subtract 1 from this:

\[
2.396558 - 1 = 1.396558
\]

Next, divide by the interest rate (0.06):

\[
\frac{1.396558}{0.06} = 23.275966
\]

Finally, multiply by the annual payment of $400:

\[
FV = 400 \times 23.275966 = 9310.39
\]

So, the future value of the investment is approximately **$9,310**, which matches one of the answer choices.

### Answer: 
The future value is **$9,310**.

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Would you like a deeper explanation or have any further questions?

Here are 5 related questions to expand your understanding:
1. What is the formula for present value of an annuity?
2. How would the future value change if the interest rate were 8% instead of 6%?
3. What happens to the future value if the investment period is extended to 20 years?
4. How would the future value be affected by making monthly contributions instead of yearly ones?
5. Can you derive a formula for the future value of an annuity due (payments at the beginning of the period)?

**Tip:** When calculating future value, increasing either the interest rate or the number of periods will generally result in a higher final amount.

What is the future value of $400 invested each year for 15 years at a rate of 6%?

Learn how to calculate the future value of $400 invested annually for 15 years at an interest rate of 6%. This detailed solution walks through the future value of annuities formula, exponential growth, and compound interest, ideal for students in Grades 10-12.

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