Work each problem. Elmer borrowed \$3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%. How much will the interest amount to?

Verified step by step guidance

1. Identify the principal amount (P), the annual interest rate (r), and the time period (t) in years. Here, P = 3150, r = 4% (which is 0.04 as a decimal), and t = 6 months (which is 0.5 years).
2. Recall the formula for simple interest: \(I = P \times r \times t\) where \(I\) is the interest.
3. Substitute the known values into the formula: \(I = 3150 \times 0.04 \times 0.5\).
4. Multiply the numbers step-by-step: first multiply the principal by the interest rate, then multiply the result by the time period in years.
5. The result from the multiplication will give the interest amount Elmer needs to pay Julio after 6 months.

Key Concepts

Simple Interest Formula

Simple interest is calculated using the formula I = P × r × 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. This formula helps determine the interest earned or paid over a specific period.

Converting Time to Years

Since interest rates are typically annual, the time period must be expressed in years. For example, 6 months is converted to 0.5 years by dividing by 12. This ensures the time variable in the interest formula is consistent with the rate.

Principal Amount

The principal is the initial amount of money borrowed or invested before interest. In this problem, the principal is $3150, which is the base amount on which the interest will be calculated.