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 $ 5000 at the end of each year in an annuity that pays 5 % compounded annually.
a.
How much will you have saved at the end of five​ years?
b.
Find the interest.

To solve this problem, we are dealing with an **ordinary annuity** where you deposit $5,000 at the end of each year. The annuity pays 5% interest compounded annually. 

We will use the **future value of an ordinary annuity formula**:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the annual payment (deposit), which is $5,000.
- $ r $ is the interest rate per period (5% or 0.05).
- $ n $ is the number of periods (5 years).

### a. Calculating the Future Value

Substitute the given values into the formula:

\[
FV = 5000 \times \frac{(1 + 0.05)^5 - 1}{0.05}
\]

### b. Finding the Interest

Once we calculate the future value, the total interest earned can be found by subtracting the total principal (the amount of deposits made) from the future value:

\[
\text{Interest} = FV - (P \times n)
\]

Let me calculate these values for you.### a. The future value of the annuity at the end of 5 years will be approximately **$27,628.16**.

### b. The total interest earned over the 5 years will be approximately **$2,628.16**.

Would you like more details on the calculation, or do you have any other questions?

Here are five related questions you might explore next:
1. How would the future value change if the interest rate increased to 6%?
2. What if you made deposits quarterly instead of annually, with the same interest rate?
3. How does the future value change if the deposit period is extended to 10 years?
4. What happens if you start with an initial lump sum, in addition to the regular deposits?
5. How much would you save if the interest was compounded monthly instead of annually?

**Tip:** The earlier you start saving in an annuity, the more significant the impact of compound interest becomes, especially over longer periods.

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 $5000 at the end of each year in an annuity that pays 5% compounded annually. a. How much will you have saved at the end of five​ years? b. Find the interest.

Learn how to calculate the future value of an annuity with $5000 annual deposits and 5% interest compounded annually. Explore the step-by-step solution to determine how much you'll save after 5 years and the total interest earned. Suitable for high school students (Grades 10-12).

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