Find the present value of the ordinary annuity. (Round your final answer to two decimal places.)
$5000/semiannual period for 8 years at 4%/year compounded semiannually

To calculate the present value (PV) of an ordinary annuity, we can use the following formula:

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

Where:
- $ P $ is the payment per period,
- $ i $ is the interest rate per period,
- $ n $ is the total number of periods.

### Given Data:
- $ P = 5000 $ (payment per semiannual period),
- 8 years, with semiannual periods, means $ n = 8 \times 2 = 16 $ periods,
- The annual interest rate is 4%, so the semiannual interest rate is $ i = \frac{4\%}{2} = 2\% = 0.02 $.

Now, let's calculate the present value.The present value of the ordinary annuity is \$67,888.55.

Would you like further details or have any questions? Here are 5 related questions to expand on this topic:

1. How does the frequency of compounding affect the present value of an annuity?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would the present value change if the interest rate were compounded monthly instead of semiannually?
4. What would be the future value of this annuity?
5. How does the length of the annuity term affect the present value?

**Tip:** Increasing the compounding frequency (e.g., from semiannually to quarterly) typically reduces the present value of an annuity, as the money is discounted more frequently.

Find the present value of the ordinary annuity. $5000/semiannual period for 8 years at 4%/year compounded semiannually.

Learn how to calculate the present value of an ordinary annuity with $5000 per semiannual period over 8 years at a 4% annual interest rate compounded semiannually. This finance problem explains key concepts like time value of money and annuities, using the present value formula. Ideal for college-level finance students.

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