Question

the principal p is borrowed at a simple interest rate r for a period of time t. find the simple interest owed for the use of the money. assume 365 days in a year p = $8000, r = 7.5%, t = 15 months, the simple interest owed for the use of the money is $\square. (do not round until the final answer. then round to the nearest cent as needed )

Explanation:

Step1: Recall simple interest formula

The formula for simple interest \( I \) is \( I = P \times r \times t \), where \( P \) is principal, \( r \) is annual interest rate (in decimal), and \( t \) is time in years.

Step2: Convert rate to decimal

Given \( r = 7.5\% \), convert to decimal: \( r=\frac{7.5}{100}=0.075 \).

Step3: Convert time to years

\( t = 15 \) months. Since 1 year = 12 months, \( t=\frac{15}{12}=\frac{5}{4}=1.25 \) years.

Step4: Calculate simple interest

Substitute \( P = 8000 \), \( r = 0.075 \), \( t = 1.25 \) into \( I = P \times r \times t \):
\( I = 8000\times0.075\times1.25 \)
First, \( 8000\times0.075 = 600 \). Then, \( 600\times1.25 = 750 \).

Answer:

\( 750.00 \)