Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
Rate
Time
​$9000 at the end of each year
5 % compounded annually
15 years
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Part 1
a. The value of the annuity is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

To find the future value $ A $ of an ordinary annuity (where deposits are made at the end of each period), we can use the following formula for an annuity compounded annually:

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

Where:
- $ P $ is the periodic deposit,
- $ r $ is the interest rate per period (expressed as a decimal),
- $ t $ is the number of periods.

### Given:
- $ P = 9000 $ (the amount deposited at the end of each year),
- $ r = 0.05 $ (5% annual interest rate),
- $ t = 15 $ years.

Now, let’s calculate the future value $ A $:

\[
A = 9000 \times \frac{(1 + 0.05)^{15} - 1}{0.05}
\]

First, compute $ (1 + 0.05)^{15} $:

\[
(1.05)^{15} = 2.078928179
\]

Now substitute back into the formula:

\[
A = 9000 \times \frac{2.078928179 - 1}{0.05}
\]
\[
A = 9000 \times \frac{1.078928179}{0.05}
\]
\[
A = 9000 \times 21.57856358
\]
\[
A = 194,207.07
\]

### Part 1 Answer:
The value of the annuity is approximately **\$194,207**.

---

### Part 2: Finding the Interest Earned

The interest earned on the annuity is the total future value minus the total amount deposited.

Total amount deposited over 15 years:
\[
9000 \times 15 = 135,000
\]

Interest earned:
\[
\text{Interest} = A - \text{Total Deposits} = 194,207.07 - 135,000 = 59,207.07
\]

### Part 2 Answer:
The interest earned is approximately **\$59,207**.

---

Would you like a more detailed explanation on any part of the calculation, or have any other questions?

### Related Questions:
1. What is the formula for the present value of an annuity?
2. How would the value change if the interest was compounded monthly?
3. What happens if the deposit amount changes each year?
4. How do different compounding periods (e.g., quarterly) affect the future value of an annuity?
5. How is the interest portion of an annuity taxed?

#### Tip:
Always convert the interest rate to a decimal when using financial formulas. For example, 5% becomes 0.05.

Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
Rate
Time
$9000 at the end of each year
5% compounded annually
15 years

Learn how to calculate the future value of an annuity with $9000 deposited at the end of each year, compounded annually at 5% for 15 years. Step-by-step solution provided, along with the interest earned. Suitable for high school and college finance students.

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