(A) If you want to have $$ \$ 300 $$ in 3 years and you can earn an annual return of $$ 6 \% $$, how much must you invest today? Be sure to use cell references and make sure that your answer appears as a positive value.

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To determine how much you need to invest today to have \$300 in 3 years with an annual return of 6%, you can use the **Present Value (PV)** formula in a spreadsheet like Microsoft Excel or Google Sheets. Below is a step-by-step guide using cell references to ensure your answer appears as a positive value.

### Step 1: Set Up Your Spreadsheet

1. **Enter the Given Values:**
   - **Annual Return (Interest Rate):**  
     - **Cell A1:** `6%`
   - **Number of Years (Periods):**  
     - **Cell A2:** `3`
   - **Future Value (Desired Amount):**  
     - **Cell A3:** `$300`

2. **Calculate the Present Value:**
   - **Cell A4:** This cell will contain the formula to calculate the present value.

### Step 2: Use the PV Function with Cell References

The **PV** function calculates the present value of an investment based on a constant interest rate and a fixed number of periods. The syntax for the PV function is:

```
PV(rate, nper, pmt, [fv], [type])
```

- **rate:** Interest rate per period.
- **nper:** Total number of payment periods.
- **pmt:** Payment made each period (set to `0` since we're dealing with a single future amount).
- **fv:** Future value (the amount you want to have in the future).
- **type:** When payments are due (optional; assume `0` for end of period).

**Formula to Enter in Cell A4:**

```excel
=PV(A1, A2, 0, A3) * -1
```

**Explanation:**
- `PV(A1, A2, 0, A3)`: Calculates the present value based on the interest rate in A1, number of periods in A2, no recurring payments (`0`), and the future value in A3.
- `* -1`: Converts the result to a positive number, as Excel's PV function typically returns a negative value to represent cash outflow.

### Step 3: Result

After entering the formula, **Cell A4** will display the present value you need to invest today.

**Calculation:**

$$
PV = \frac{\$300}{(1 + 0.06)^3} \approx \frac{\$300}{1.191016} \approx \$251.35
$$

**Final Answer:**

You need to invest **\$251.35** today to have \$300 in 3 years at an annual return of 6%.

### Example Spreadsheet Layout

| **Cell** | **Description**          | **Value** |
|----------|--------------------------|-----------|
| A1       | Annual Return (Rate)     | 6%        |
| A2       | Number of Years (Periods)| 3         |
| A3       | Future Value (FV)        | $300      |
| A4       | Present Value (PV)       | =PV(A1, A2, 0, A3)*-1 → **$251.35** |

---

**Note:** Ensure that the cells are formatted appropriately (e.g., percentage for the rate, currency for the amounts) to display the values correctly.
You need to invest \$251.35 today to have \$300 in 3 years at an annual return of 6%.

(A) If you want to have in 3 years and you can earn an annual return of ,
how much must you invest today? Be sure to use cell references and make sure
that your answer appears as a positive value.

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(A) If you want to have in 3 years and you can earn an annual return of , how much must you invest today? Be sure to use cell references and make sure that your answer appears as a positive value.