burnett needs $7,000 in three years to make the down - payment on a new car. how much must she invest today…

burnett needs $7,000 in three years to make the down - payment on a new car. how much must she invest today if she receives 0.5% interest annually, compounded annually? click the icon to view the present value of $1.00 table. must invest $6,694.2. (round to the nearest cent as needed.)

burnett needs $7,000 in three years to make the down - payment on a new car. how much must she invest today if she receives 0.5% interest annually, compounded annually? click the icon to view the present value of $1.00 table. must invest $6,694.2. (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the present - value formula

The formula for present value $PV$ when compounded annually is $PV=\frac{FV}{(1 + r)^n}$, where $FV$ is the future value, $r$ is the annual interest rate, and $n$ is the number of years.

Step2: Assign values to variables

We have $FV = 7000$, $r=0.005$ (since $0.5%=0.005$), and $n = 3$.

Step3: Calculate the present value

$PV=\frac{7000}{(1 + 0.005)^3}=\frac{7000}{1.005^3}=\frac{7000}{1.015075125}\approx6896.20$

Answer:

$$6896.20$