Question

in order to start a small business, a student takes out a simple interest loan for $5000 for 6 months at a rate of 8.25%.
a. how much interest must the student pay?
b. find the future value of the loan.

a. the amount of interest is $\square$.
(round to the nearest cent as needed.)

Explanation:

Step1: Recall simple interest formula

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

Step2: Convert values to appropriate units

• Principal \( P = \$5000 \)
• Annual interest rate \( r = 8.25\% = 0.0825 \) (converted to decimal by dividing by 100)
• Time \( t = 6 \) months. Since there are 12 months in a year, \( t = \frac{6}{12} = 0.5 \) years.

Step3: Calculate the interest

Substitute the values into the formula: \( I = 5000 \times 0.0825 \times 0.5 \)
First, calculate \( 5000 \times 0.0825 = 412.5 \)
Then, calculate \( 412.5 \times 0.5 = 206.25 \)

Answer:

\( 206.25 \)