(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.

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.