Question

the principal p is borrowed and the loans future value a at time t is given. determine the loans simple interest rate r. p = $9000.00, a = $9405.00, t = 1 year. % (round to the nearest tenth of a percent as needed.)

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula 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 $P = 9000$, $A = 9405$, and $t = 1$. Substitute these values into the formula for $r$: $r=\frac{9405 - 9000}{9000\times1}$.

Step3: Calculate the numerator

$9405−9000 = 405$. So, $r=\frac{405}{9000\times1}=\frac{405}{9000}$.

Step4: Simplify the fraction and convert to percentage

$\frac{405}{9000}=0.045$. To convert to a percentage, multiply by 100: $r = 0.045\times100 = 4.5\%$.

Answer:

$4.5$