the principal p is borrowed and the loans future value a at time t is given. determine the loans simple…

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 principal, $r$ is the interest rate, and $t$ is the time in years. We can rewrite it to solve for $r$: $r=\frac{A - P}{Pt}$.

Step2: Substitute given values

Given $P = 2000$, $A = 2420$, and $t = 3$. Substitute these values into the formula: $r=\frac{2420 - 2000}{2000\times3}$.

Step3: Calculate the numerator

$2420−2000 = 420$. So, $r=\frac{420}{2000\times3}$.

Step4: Calculate the denominator

$2000\times3=6000$. So, $r=\frac{420}{6000}$.

Step5: Simplify the fraction

$r = 0.07$ or $7%$.

Answer:

$7%$