Problem
Question 20 3 pts 5 Details ${ }^{\star}$ Clearly show your work for this question on your paper. Suppose you are planning ahead to purchase a car. You anticipate you will need $\$ 10,500$ for the car, and want to be ready to purchase it in 9 years. How much do you need to invest NOW (this is called the present value) at an annual simple interest rate of $5.1 \%$ in order to have the amount you need for the car in 9 years? Present value $=\$$ Give your answer rounded to 2 decimal places Submit Question
Solution
Step 1 ：Define the variables: the future value (A) is $10500, the interest rate (r) is 0.051, and the number of years (t) is 9.
Step 2 ：Calculate the present value (P) using the formula \(P = \frac{A}{1 + rt}\).
Step 3 ：Substitute the values into the formula: \(P = \frac{10500}{1 + 0.051 \times 9}\).
Step 4 ：Solve the equation to find the present value (P).
Step 5 ：The present value you need to invest now is approximately $7196.71.
Step 6 ：So, the final answer is \(\boxed{7196.71}\).
