Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
Rate
Time
​$90 at the end of every six months
4.5 % compounded semiannually
30 years
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Part 1
a. The value of the annuity is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

To find the value of the annuity, we can use the **Future Value of an Ordinary Annuity Formula**:

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

Where:
- $FV$ is the future value of the annuity (the value we are solving for),
- $P$ is the periodic deposit,
- $r$ is the interest rate per period,
- $n$ is the total number of periods.

Let's plug in the information given:

- Periodic Deposit, $P = 90$,
- Rate per period, $r = \frac{4.5\%}{2} = 0.0225$ (since the rate is compounded semiannually),
- Time, 30 years, so total periods $n = 30 \times 2 = 60$.

Now, using the formula:

\[
FV = 90 \times \left( \frac{(1 + 0.0225)^{60} - 1}{0.0225} \right)
\]

We can compute this value to find the future value of the annuity.

Let me calculate that.The future value of the annuity is approximately **$11,201** when rounded to the nearest dollar.

### Part 2: Finding the interest

The total interest earned can be found by subtracting the total deposits from the future value of the annuity. The total deposits are simply the periodic deposit multiplied by the total number of periods.

\[
\text{Total Deposits} = P \times n = 90 \times 60
\]

\[
\text{Interest} = FV - \text{Total Deposits}
\]

Let me calculate that.The total interest earned on the annuity is approximately **$5,801**.

Would you like more details on these calculations, or do you have any questions?

Here are some related questions:
1. How would the future value change with a different interest rate?
2. What is the impact of compounding more frequently (e.g., quarterly)?
3. How does the number of years affect the future value of an annuity?
4. What is the formula for finding the present value of an annuity?
5. How would this calculation differ if deposits were made at the beginning of each period?

**Tip**: The more frequently the interest is compounded, the more interest you'll earn over time due to the compounding effect.

Use the appropriate formula to find the value of the annuity. Find the interest. Periodic Deposit: $90 at the end of every six months, Rate: 4.5% compounded semiannually, Time: 30 years.

Learn how to calculate the future value and interest earned from an annuity with a $90 semiannual deposit, 4.5% interest compounded semiannually, over a period of 30 years. Understand the key formulas and steps for solving annuity problems. Suitable for advanced high school and college students.

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