Question

the principal p is borrowed at a simple interest rate r for a period of time t. find the loans future value a, or the total amount due at time t. p = $1000, r = 4%, t = 3 years $\square$ (round to the nearest cent as needed.)

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is \( I = P \times r \times t \), and the future value \( A \) (total amount) is \( A = P + I = P(1 + rt) \). Here, \( P = 1000 \), \( r = 4\% = 0.04 \), and \( t = 3 \).

Step2: Substitute values into the formula

Substitute \( P = 1000 \), \( r = 0.04 \), and \( t = 3 \) into \( A = P(1 + rt) \):
\( A = 1000\times(1 + 0.04\times3) \)

Step3: Calculate inside the parentheses first

Calculate \( 0.04\times3 = 0.12 \), then \( 1 + 0.12 = 1.12 \).

Step4: Multiply by principal

Multiply \( 1000 \times 1.12 = 1120 \).

Answer:

\( \$1120.00 \)