Find the present value of an ordinary annuity with deposits of $22,742 quarterly for 8 years at 6.8% compounded quarterly 

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

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

Where:
- $PV$ = Present value of the annuity
- $P$ = Payment amount per period (in this case, $22,742$)
- $r$ = Interest rate per period
- $n$ = Total number of periods

### Given information:
- Quarterly payment ($P$) = \$22,742
- Annual interest rate = 6.8%
- Compounded quarterly, so quarterly interest rate $r = \frac{6.8\%}{4} = 0.017 = 1.7\%$
- The duration is 8 years, with quarterly payments. So the total number of periods $n = 8 \times 4 = 32$

Now we can calculate the present value using the formula.

Let me do the calculation for you.The present value of the ordinary annuity is approximately **$557,738.42**.

Would you like further clarification on the steps or details about the calculation?

Here are 5 related questions you might find useful:
1. How does the present value change if the interest rate increases?
2. What is the future value of this annuity after 8 years?
3. How does an ordinary annuity differ from an annuity due in terms of present value?
4. How does the number of compounding periods affect the present value?
5. What happens if the payment amount is adjusted annually instead of quarterly?

**Tip:** For annuities, the frequency of compounding plays a key role in both the present and future value calculations. Always align the interest rate and number of periods with the payment frequency.

Find the present value of an ordinary annuity with deposits of $22,742 quarterly for 8 years at 6.8% compounded quarterly

Learn how to calculate the present value of an ordinary annuity with quarterly deposits of $22,742 for 8 years at a 6.8% annual interest rate compounded quarterly. This problem covers the key concepts of annuities, present value, and compound interest. Suitable for high school students in Grades 10-12.

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