Sam Sounds received a $290 discount loan to purchase a stereo. The loan was offered at 16% for 90 days. Find the interest in dollars and the proceeds for the following problem.

Question

The interest is $
.

The proceeds are $
.

Answer 1

To calculate the interest and the proceeds from the discount loan, we can follow these steps:

1. Calculate the interest: The formula for calculating the interest on a discount loan is: \[ \text{Interest} = \text{Loan Amount} \times \text{Rate} \times \text{Time} \] where:

   • The Loan Amount is the amount of the discount ($290)
   • The Rate is the annual interest rate (16%, or 0.16)
   • The Time is the duration of the loan in years (90 days, which is \(\frac{90}{360} = 0.25\) years)

   Plugging in the values: \[ \text{Interest} = 290 \times 0.16 \times 0.25 = 290 \times 0.04 = 11.60 \]

2. Calculate the proceeds: The proceeds of the loan can be calculated by subtracting the interest from the loan amount: \[ \text{Proceeds} = \text{Loan Amount} - \text{Interest} \] \[ \text{Proceeds} = 290 - 11.60 = 278.40 \]

Thus, the interest and proceeds can be reported as follows:

• The interest is $11.60.
• The proceeds are $278.40.