36 monthy payments of 325 in an account where the interest rate is 3.5% compounded monthy find the present vaule of the annuity  

To find the present value of an annuity with monthly payments, we can use the formula:

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

Where:
- $ PV $ = Present value of the annuity (what we want to find)
- $ P $ = Payment amount per period (\$325)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments

Let's plug in the values:
- $ P = 325 $
- Annual interest rate = 3.5%, so the monthly interest rate is $ r = \frac{3.5\%}{12} = 0.00291667 $
- $ n = 36 $ (36 monthly payments)

Now I'll calculate the present value.

The present value of the annuity is approximately **\$11,091.36**.

Would you like more details or have any questions?

Here are five related questions you might explore:
1. How does changing the interest rate affect the present value of the annuity?
2. What would happen to the present value if the number of payments increased?
3. How is the formula for the present value of an annuity derived?
4. What is the difference between the present value of an annuity and the future value?
5. How does monthly compounding impact the growth of an investment over time?

**Tip:** Increasing the frequency of compounding (e.g., monthly vs annually) slightly increases the effective interest rate.

36 monthly payments of 325 in an account where the interest rate is 3.5% compounded monthly. Find the present value of the annuity.

Calculate the present value of an annuity with 36 monthly payments of $325 at a 3.5% interest rate compounded monthly. This problem covers annuities, compound interest, and the present value formula. Suitable for advanced high school or college-level students.

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