determine the present value p that must be invested to have the future value a at simple interest rate r…

Explanation:

Step1: Recall simple - interest formula

The formula for simple - interest is $A = P(1+rt)$, where $A$ is the future value, $P$ is the present value, $r$ is the interest rate, and $t$ is the time. We need to solve for $P$. Rearranging the formula gives $P=\frac{A}{1 + rt}$.

Step2: Convert the interest rate to decimal

Given $r = 3.5%=0.035$, $t = 3$ years, and $A=$7000$.

Step3: Substitute values into the formula

$P=\frac{7000}{1+(0.035\times3)}$. First, calculate the value inside the parentheses: $0.035\times3 = 0.105$. Then $1+(0.035\times3)=1 + 0.105=1.105$. So, $P=\frac{7000}{1.105}\approx$6334.84$.

Answer:

$$6334.84$