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 = $9945.00, t = 3 years

□% (round to the nearest tenth of a percent as needed )

Explanation:

Step1: Recall simple interest formula

The formula for simple interest future value is \( A = P(1 + rt) \), where \( A \) is future value, \( P \) is principal, \( r \) is rate, \( t \) is time.

Step2: Substitute values into formula

Substitute \( P = 9000 \), \( A = 9945 \), \( t = 3 \) into \( A = P(1 + rt) \):
\( 9945 = 9000(1 + 3r) \)

Step3: Solve for \( r \)

First, divide both sides by 9000:
\( \frac{9945}{9000} = 1 + 3r \)
Simplify \( \frac{9945}{9000} = 1.105 \), so:
\( 1.105 = 1 + 3r \)
Subtract 1: \( 0.105 = 3r \)
Divide by 3: \( r = \frac{0.105}{3} = 0.035 \)

Step4: Convert to percentage

Multiply by 100: \( r = 0.035 \times 100 = 3.5\% \)

Answer:

\( 3.5\% \)