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: \( I = P \times r \times t \), where \( I \) is the interest, \( P \) is the principal amount, \( r \) is the rate of interest per year, and \( t \) is the time in years.
2. Substitute the given values into the formula: \( P = 500 \), \( r = 0.02 \) (since 2% as a decimal is 0.02), and \( t = 4 \).
3. Calculate the interest by multiplying the principal \( P \) by the rate \( r \) and the time \( t \): \( I = 500 \times 0.02 \times 4 \).
4. Perform the multiplication step by step: first calculate \( 500 \times 0.02 \), then multiply the result by 4.
5. The result from the previous step will give you the total interest earned over the 4 years.

Key Concepts

Simple Interest Formula

The simple interest formula is used to calculate the interest earned on an investment over time. It is expressed as I = PRT, where I is the interest, P is the principal amount (initial investment), R is the rate of interest (as a decimal), and T is the time in years. This formula allows for straightforward calculations of interest without compounding.

Principal Amount

The principal amount refers to the initial sum of money that is invested or loaned. In this context, it is the $500 that the person invests. Understanding the principal is crucial because it serves as the base amount upon which interest is calculated, directly affecting the total interest earned over time.

Interest Rate

The interest rate is the percentage at which interest is calculated on the principal amount. In this problem, the interest rate is 2%, which means that for every dollar invested, 2 cents will be earned as interest each year. This rate is essential for determining how much interest accumulates over the specified time period.