An investor can make an investment in a real estate development and receive an expected cash return of $45,000 at the end of six years. Based on a careful study of other investment alternatives, she believes that a 9 percent annual return compounded quarterly is a reasonable return to earn on this investment.

Required:
How much should she pay for the investment today?

To determine how much the investor should pay for the investment today, we need to calculate the present value of the expected cash return, given that the cash flow is received at the end of six years and the annual return is 9%, compounded quarterly.

The formula for the present value $ PV $ with compound interest is:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ FV $ is the future value (the expected cash return), which is $45,000.
- $ r $ is the annual interest rate (9% or 0.09).
- $ n $ is the number of compounding periods per year (quarterly compounding means $ n = 4 $).
- $ t $ is the number of years (6 years).
- $ PV $ is the present value (how much the investment is worth today).

### Step-by-Step Calculation:
1. **Future Value (FV)**: $ 45,000 $
2. **Interest Rate (r)**: $ 0.09 $
3. **Number of Compounding Periods (n)**: $ 4 $
4. **Number of Years (t)**: $ 6 $

Now, plug these values into the formula:

\[
PV = \frac{45,000}{(1 + \frac{0.09}{4})^{4 \times 6}} = \frac{45,000}{(1 + 0.0225)^{24}}
\]

\[
PV = \frac{45,000}{(1.0225)^{24}}
\]

\[
PV = \frac{45,000}{1.684134} \approx 26,723.99
\]

### Conclusion:
The investor should pay approximately **$26,723.99** for the investment today.

---

Would you like further details on any step or have any questions? Here are some related questions that you may find useful:

1. How is quarterly compounding different from annual compounding?
2. What if the interest rate were compounded monthly instead of quarterly?
3. How would a change in the expected cash return affect the present value?
4. What is the significance of discounting future cash flows in investment decisions?
5. How would the calculation change if the interest rate were variable?

**Tip:** Compounding more frequently (e.g., quarterly vs. annually) results in a slightly lower present value, as interest is earned on a more frequent basis.

An investor can make an investment in a real estate development and receive an expected cash return of $45,000 at the end of six years. Based on a careful study of other investment alternatives, she believes that a 9 percent annual return compounded quarterly is a reasonable return to earn on this investment. How much should she pay for the investment today?

Learn how to calculate the present value of an investment in real estate with a future cash return of $45,000, using a 9% annual interest rate compounded quarterly. This step-by-step guide demonstrates the use of the compound interest formula for determining present value, ideal for students in Grades 10-12.

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