Find the present value of an annuity of $7000 paid at the end of each 6-month period for 10 years if the interest rate is 6%, compounded semiannually. (Round your answer to the nearest cent.)

To find the present value of an annuity, we use the Present Value of an Ordinary Annuity formula:

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

Where:
- $ PV $ = Present Value of the annuity (the value we want to find)
- $ P $ = Payment per period ($7,000)
- $ r $ = Interest rate per period
- $ n $ = Number of periods per year
- $ t $ = Total number of years

### Step 1: Determine the given values
- $ P = 7,000 $
- Interest rate per year is 6%, so the semiannual rate is $ r = \frac{6\%}{2} = 0.03 $ (since the interest is compounded semiannually)
- Number of periods per year: $ n = 2 $ (because the annuity is paid semiannually)
- Time $ t = 10 $ years, so the total number of periods $ nt = 2 \times 10 = 20 $

### Step 2: Plug the values into the formula

\[
PV = 7000 \times \frac{1 - (1 + 0.03)^{-20}}{0.03}
\]

Let me calculate this value for you.The present value of the annuity is approximately **$104,142.32**.

Would you like further details on the steps, or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the present value change if the interest rate were higher?
2. What is the future value of this same annuity?
3. How does the concept of discounting relate to the present value?
4. What if the payments were made at the beginning of each period (annuity due)?
5. How does the number of periods affect the present value?

**Tip:** Increasing the interest rate or reducing the number of periods decreases the present value of an annuity, as the money is discounted more heavily.

Discover how to calculate the present value of an annuity of $7000 paid semiannually for 10 years at a 6% interest rate, compounded semiannually. This solution explains the Present Value of an Ordinary Annuity formula and demonstrates the step-by-step process for calculating the answer. Perfect for finance students and professionals.

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