# Finance Problem: Time Value of Money ## Problem Statement Sarah wants to buy a car in 5 years. She estimates that she will need $20,000 for her purchase. To reach her goal, she decides to deposit a certain amount of money today into a savings account that earns an annual interest rate of 6%, compounded annually. **Question:** How much money should Sarah deposit today so that she will have exactly $20,000 in 5 years? ## Information Provided - **Future Value (FV):** $20,000 - **Annual Interest Rate (r):** 6% (or .06) - **Number of Years (n):** 5 - **Compounding:** Annually - **Present Value (PV):** Unknown (what Sarah needs to deposit today) ## Steps Required to Solve 1. **Write the time value of money formula for present value:** \[ PV = \frac{FV}{(1 + r)^n} \] 2. **Identify the variables:** - \( FV = \$20,000 \) - \( r = .06 \) - \( n = 5 \) 3. **Substitute the values into the formula.** 4. **Calculate the denominator: \((1 + r)^n\)** 5. **Divide the FV by the result from Step 4 to get PV.** --- **Show all your work and round your answer to the nearest dollar.**