Find the present value of an ordinary annuity with deposits of 25,000 semiannually for 6 years at 10.8% compounded semiannually

To find the present value of an ordinary annuity, we can use the formula:

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

Where:
- $ PV $ = Present Value of the annuity
- $ P $ = Payment per period (25,000)
- $ r $ = Periodic interest rate
- $ n $ = Number of periods per year
- $ t $ = Number of years

Given:
- $ P = 25,000 $
- Annual interest rate = 10.8% or 0.108
- Compounded semiannually, so $ n = 2 $
- Number of years $ t = 6 $

Let's calculate the periodic interest rate ($ r $) and the total number of periods ($ nt $):

\[
r = \frac{0.108}{2} = 0.054
\]
\[
nt = 2 \times 6 = 12
\]

Now, plug these values into the formula:

\[
PV = 25,000 \times \frac{1 - (1 + 0.054)^{-12}}{0.054}
\]

Let's calculate the present value.The present value of the ordinary annuity is approximately \$216,666.08.

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

Here are 8 related questions you might find useful:
1. How does the present value of an annuity differ from the future value?
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 quarterly?
4. What happens to the present value if the number of years is increased?
5. How does compounding frequency affect the present value of an annuity?
6. Can you calculate the future value of this annuity?
7. How does the payment amount affect the present value?
8. What is the impact of a changing interest rate on the present value?

**Tip:** Understanding the impact of different compounding periods on an annuity's present value can help in making better financial decisions.

Learn how to calculate the present value of an ordinary annuity with deposits of $25,000 semiannually for 6 years at a 10.8% interest rate compounded semiannually. Understand the formula used and step-by-step calculation process. Suitable for advanced college-level students and financial professionals.

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