Question

tony opened a hot - dog stand last april. he borrowed $6100 to pay for the stand and startup inventory, and he agreed to pay off the loan in 10 months at 7% simple interest. find the total amount required to repay the loan. the total amount required to repay the loan is $\square$ (simplify your answer. type an integer or decimal rounded 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 \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years. The total amount \( A \) to repay is \( A = P + I \).

Step2: Identify values

Given \( P = \$6100 \), \( r = 7\% = 0.07 \), and \( t = \frac{10}{12} \) years (since 10 months is \( \frac{10}{12} \) of a year).

Step3: Calculate interest

Substitute into the interest formula: \( I = 6100 \times 0.07 \times \frac{10}{12} \).
First, calculate \( 6100 \times 0.07 = 427 \).
Then, \( 427 \times \frac{10}{12} = \frac{4270}{12} \approx 355.8333 \).

Step4: Calculate total amount

Add principal and interest: \( A = 6100 + 355.8333 \approx 6455.83 \).

Answer:

\( 6455.83 \)