Calculate Simple Interest

Understand the concept

In the simple-interest model, interest is calculated on the original principal rather than on an increasing balance. If the principal and rate remain unchanged, each equal period adds the same interest amount. This lesson treats a mathematical model without fees, taxes or changes to the principal.

Let P be the principal, r the percentage rate per year, and t the time in years. The simple interest is I = P × r × t / 100. The final amount is A = P + I. If the rate is written as a decimal instead of a percentage, use I = P × decimal rate × t and do not divide by 100 again.

The rate's period determines the unit of time. For an annual rate, six months is 0.5 years and eighteen months is 1.5 years. Converting the time first prevents the interest from being multiplied by twelve accidentally. For a rate stated per month, use months instead. A question involving days must specify the year basis or counting convention; do not silently assume one.

Simple interest is proportional to each factor when the others are held fixed. Doubling the principal doubles the interest, doubling the rate doubles the interest, and doubling the time doubles the interest. These proportional checks are useful when reviewing a calculation.

Do not confuse simple and compound interest. Under annual compounding, the amount after a whole number of years is P × (1 + r/100) raised to the number of years. That is a different model because accumulated interest can earn further interest. Always identify the stated interest model before calculating.

Worked example

Find the simple interest and final amount for a principal of 5,000 units at 6 percent per year for 18 months.

Convert the time: 18/12 = 1.5 years. Interest for one year is 5,000 × 6/100 = 300 units. For 1.5 years, the interest is 300 × 1.5 = 450 units.

The formula gives the same result: I = 5,000 × 6 × 1.5 / 100 = 450. The final amount is 5,000 + 450 = 5,450 units. The interest is 9 percent of the principal over the full eighteen months, since 6 percent per year × 1.5 years = 9 percent.

Practice and answer

1. Find the simple interest on 8,000 units at 5 percent per year for 9 months.
Answer: t = 9/12 = 0.75 years. I = 8,000 × 5 × 0.75 / 100 = 300 units. The final amount is 8,300 units.

2. Simple interest of 360 units is earned on 3,000 units at 4 percent per year. Find the time.
Answer: t = 360 × 100/(3,000 × 4) = 3 years.

3. Why must time units match the rate period?
Answer: the rate measures interest per stated period. Using a number of months with an annual rate treats each month as a whole year and overstates the result.

What you will learn

• Distinguish principal, interest and final amount.
• Convert time to the rate period.
• Check a simple-interest result using proportional reasoning.