Question

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.

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**.