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To find the present value of an ordinary annuity with regular quarterly payments, we’ll use the present value of an annuity formula:

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

where:
- $ PV $ = Present Value (what we’re solving for)
- $ PMT $ = Quarterly payment amount = $22,380
- $ i $ = Quarterly interest rate
- $ n $ = Total number of payments

Given:
- Quarterly payments for 4 years, which means $ n = 4 \times 4 = 16 $ payments.
- Annual interest rate of 8.4%, compounded quarterly, so $ i = \frac{8.4\%}{4} = 0.021 $ (or 2.1% per quarter).

Substitute these values into the formula:

\[
PV = 22,380 \times \frac{1 - (1 + 0.021)^{-16}}{0.021}
\]

Let's calculate this:

1. **Calculate $ (1 + 0.021)^{-16} $:**
   \[
   (1 + 0.021)^{-16} \approx 0.7025
   \]

2. **Calculate $ 1 - 0.7025 $:**
   \[
   1 - 0.7025 = 0.2975
   \]

3. **Divide by the interest rate $ 0.021 $:**
   \[
   \frac{0.2975}{0.021} \approx 14.1667
   \]

4. **Multiply by the payment $ PMT = 22,380 $:**
   \[
   PV = 22,380 \times 14.1667 \approx 316,962.63
   \]

So, the present value of this annuity is approximately **$316,962.63**.

Would you like further explanation, or do you have questions about any step?

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### Related Questions
1. How does changing the interest rate affect the present value of an annuity?
2. What would the present value be if payments were monthly instead of quarterly?
3. How does an increase in the number of payments impact the present value?
4. How does this formula differ from calculating future value for an annuity?
5. What are some real-life applications of annuity calculations?

### Tip:
In financial calculations, always double-check interest rates and compounding periods to ensure they align with the payment frequency.

Find the present value of an ordinary annuity with payments of $22,380 quarterly for 4 years at 8.4% compounded quarterly.

Calculate the present value of an ordinary annuity with quarterly payments of $22,380 over 4 years at an interest rate of 8.4% compounded quarterly. This solution covers key financial concepts, including the present value of annuities and compound interest calculations.

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