Suppose that you earned a bachelor's degree and now you're teaching high school.The school district offers teachers the opportunity to take a year off to earna master's degree. To achieve this goal, you deposit $2000 at the end of each yearin an annuity that pays 4.5% compounded annually a. After 5 years, you will have approximately $?

To determine how much you'll have in the annuity after 5 years, we can use the formula for the future value of an ordinary annuity. The formula is:

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

Where:
- $ FV $ = future value of the annuity
- $ P $ = annual deposit (in this case, $2000)
- $ r $ = interest rate per period (4.5% annually, or 0.045)
- $ n $ = number of periods (5 years)

Let’s compute this.

\[
FV = 2000 \times \frac{(1 + 0.045)^5 - 1}{0.045}
\]

First, calculate $ (1 + 0.045)^5 $:

\[
(1 + 0.045)^5 = 1.045^5 \approx 1.2467
\]

Now, subtract 1 from this value:

\[
1.2467 - 1 = 0.2467
\]

Now, divide by the interest rate $ r = 0.045 $:

\[
\frac{0.2467}{0.045} \approx 5.4822
\]

Finally, multiply by the annual deposit of $2000:

\[
FV = 2000 \times 5.4822 = 10,964.40
\]

So, after 5 years, you will have approximately **$10,964.40** in the annuity.

Would you like further details or have any questions?

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Here are five related questions:
1. How would the amount change if you contributed $2500 annually?
2. What if the interest rate was increased to 5%?
3. How much would you have after 10 years under the same conditions?
4. How would semi-annual compounding affect the future value?
5. What is the total amount of contributions over the 5 years?

**Tip**: Increasing the number of periods or the interest rate increases the power of compounding.

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $2000 at the end of each year in an annuity that pays 4.5% compounded annually. After 5 years, you will have approximately $?

Learn how to calculate the future value of an annuity with a $2000 annual deposit at an interest rate of 4.5% compounded annually. This problem uses the future value of an ordinary annuity formula and involves concepts of compound interest. Suitable for high school students in Grades 10-12.

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