A consulting project will generate revenue of $20,980.00 per quarter for a 4.00-year period. If the consulting firm wants an 8.84% APR (with quarterly compounding) return on their projects, what is the value of the project to the firm today?

To calculate the value of the consulting project today, we need to find the **present value of an annuity**. The project generates quarterly payments of $20,980.00 for 4 years, and we are given the annual percentage rate (APR) of 8.84%, compounded quarterly.

### Steps:

1. **Determine the total number of periods (n)**:
   Since the payments are made quarterly for 4 years, the total number of quarters is:
   \[
   n = 4 \, \text{years} \times 4 \, \text{quarters per year} = 16 \, \text{quarters}.
   \]

2. **Convert the APR to the quarterly interest rate (r)**:
   The APR is 8.84% annually, but the interest is compounded quarterly. To find the quarterly rate, divide the APR by 4:
   \[
   r = \frac{8.84\%}{4} = 2.21\% = 0.0221.
   \]

3. **Use the present value of an annuity formula**:
   The present value $ PV $ of an annuity is calculated using the formula:
   \[
   PV = P \times \left( 1 - \frac{1}{(1 + r)^n} \right) \div r
   \]
   where:
   - $ P $ is the quarterly payment ($20,980),
   - $ r $ is the quarterly interest rate (0.0221),
   - $ n $ is the number of periods (16 quarters).

Let's now calculate the present value.The present value of the consulting project to the firm today is approximately **$280,178.18**.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would the present value change if the interest rate were 10% APR?
2. What would be the future value of the project after 4 years, given the same payments and interest rate?
3. How would the present value change if the payments were monthly instead of quarterly?
4. What is the impact of reducing the project length to 3 years on the present value?
5. How would you calculate the effective annual rate (EAR) from the given APR?

**Tip:** When interest is compounded quarterly, always divide the APR by 4 to get the quarterly interest rate.

Calculate the present value of a consulting project generating $20,980 in quarterly payments over 4 years, given an 8.84% APR with quarterly compounding. Learn how to apply the present value of annuity formula, suitable for advanced finance students.

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