Solve each problem. If a person invests \$500 at 2% simple interest for 4 yr, how much interest is earned?

Verified step by step guidance

1. Identify the formula for simple interest, which is given by \(I = P \times r \times t\), where \(I\) is the interest earned, \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), and \(t\) is the time in years.
2. Substitute the given values into the formula: the principal \(P = 500\), the interest rate \(r = 2\% = 0.02\), and the time \(t = 4\) years.
3. Set up the expression for the interest earned as \(I = 500 \times 0.02 \times 4\).
4. Multiply the numbers step-by-step: first multiply the principal by the interest rate, then multiply the result by the time period.
5. The final product will give the total simple interest earned over the 4 years.

Key Concepts

Simple Interest Formula

Simple interest is calculated using the formula I = P × r × t, where I is the interest earned, P is the principal amount invested, r is the annual interest rate (expressed as a decimal), and t is the time in years. This formula helps determine the total interest earned over a specific period.

Principal Amount

The principal is the initial amount of money invested or loaned. In this problem, the principal is $500, which is the base amount on which interest is calculated. Understanding the principal is essential to apply the interest formula correctly.

Interest Rate and Time Period

The interest rate is the percentage charged or earned annually, expressed as a decimal in calculations (e.g., 2% = 0.02). The time period is the duration the money is invested or borrowed, measured in years. Both factors directly affect the total interest earned.