A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.

Regular deposit:	$650
Interest rate:	2.25%
Frequency	monthly
Time:	25 years

To find out how much the annuity will hold at the end of 25 years, we can use the **future value of an ordinary annuity formula**:

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

Where:
- $ FV $ = future value of the annuity
- $ P $ = regular deposit (\$650)
- $ r $ = annual interest rate (2.25% or 0.0225)
- $ n $ = number of times the interest is compounded per year (monthly = 12)
- $ t $ = number of years (25 years)

### Step-by-step:

1. Convert the interest rate to a decimal: $ r = 0.0225 $.
2. The interest is compounded monthly, so $ n = 12 $.
3. The time period is 25 years, so $ t = 25 $.

Now plug the values into the formula:

\[
FV = 650 \times \left( \frac{(1 + 0.0225/12)^{12 \times 25} - 1}{0.0225/12} \right)
\]

Let me calculate this.The annuity will hold approximately **$261,432** at the end of 25 years.

Would you like more details on how this was calculated or have any questions?

Here are 5 related questions for further exploration:
1. How does increasing the interest rate affect the future value of the annuity?
2. What if the deposits were made quarterly instead of monthly? How would that change the result?
3. How much would the annuity hold if the time period were extended to 30 years?
4. What happens if the deposit amount is increased to $800 per month?
5. How can you calculate the total amount of interest earned on the annuity?

**Tip**: The frequency of compounding significantly impacts the growth of an annuity—more frequent compounding leads to faster growth.

A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.

Regular deposit: $650
Interest rate: 2.25%
Frequency: monthly
Time: 25 years

Calculate how much an annuity will hold after 25 years with monthly $650 deposits and an interest rate of 2.25%. This example covers compound interest, exponential growth, and the future value of an ordinary annuity formula. Ideal for high school students studying financial math.

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