Question 20
3 pts
5
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${ }^{\star}$ 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
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Answer

So, the final answer is $\boxed{7196.71}$.

Steps

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 $\boxed{7196.71}$.