Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
Rate
Time
​$70 at the end of each month
5 % compounded monthly
25 years
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Part 1
a. The value of the annuity is ​$

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 use the formula for the future value of an ordinary annuity (where deposits are made at the end of each period):

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

Where:
- $ A $ is the future value of the annuity.
- $ P $ is the periodic deposit.
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time in years.

### Given:
- $ P = 70 $ (the periodic deposit).
- $ r = 0.05 $ (the interest rate as a decimal, 5%).
- $ n = 12 $ (since the interest is compounded monthly).
- $ t = 25 $ years.

#### Step 1: Plug the values into the formula

\[
A = 70 \times \frac{(1 + 0.05/12)^{12 \times 25} - 1}{0.05/12}
\]

Let's calculate this.The value of the annuity is approximately **$41,686**.

### Part 2: Finding the interest

The total interest earned is the difference between the future value of the annuity and the total deposits made.

1. Total deposits = $ P \times n \times t $
2. Interest = Future value of the annuity - Total deposits

Let's calculate the interest.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the total interest manually using the following steps:

1. **Total deposits**: $ P \times n \times t = 70 \times 12 \times 25 = 21,000 $
2. **Interest**: Subtract the total deposits from the future value of the annuity:
   \[
   \text{Interest} = 41,686 - 21,000 = 20,686
   \]

The interest earned on the annuity is approximately **$20,686**.

Let me know if you have any questions or would like further details!

### Related questions:
1. How would the future value change if the interest rate were 6% instead of 5%?
2. What would be the future value if the time period was 30 years instead of 25 years?
3. How does compounding annually differ from compounding monthly in terms of annuity growth?
4. What is the impact of increasing the periodic deposit to $100?
5. How do you calculate the present value of an annuity?

**Tip**: Regular small deposits can grow significantly over time with compound interest.

Use the appropriate formula to find the value of the annuity. Periodic Deposit: $70 at the end of each month, Rate: 5% compounded monthly, Time: 25 years. a. The value of the annuity is ​$. (Do not round until the final answer. Then round to the nearest dollar as​ needed.)

Learn how to calculate the future value of an annuity with $70 monthly deposits at a 5% interest rate, compounded monthly for 25 years. This step-by-step guide includes the annuity formula and explains how to compute both the future value and total interest earned. Suitable for advanced high school or college-level students.

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