How to Solve Simple Interest Problems? (+FREE Worksheet!)

Simple interest is the most straightforward way to calculate the cost of borrowing money or the earnings on a savings account. Unlike compound interest, simple interest is calculated only on the original principal — making it easy to understand and compute. This lesson explains the formula, all four variables, and walks you through worked examples with practice problems.

What Is Simple Interest?

Simple interest is interest computed solely on the principal (the original amount), not on previously earned interest. It is used in short-term loans, some savings accounts, and many real-world financial calculations.

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The Simple Interest Formula

\(\color{blue}{I = P \times r \times t}\)

Where:

• I = Interest earned or paid (in dollars)
• P = Principal (initial amount, in dollars)
• r = Annual interest rate (as a decimal; divide the percent by 100)
• t = Time (in years)

The total amount (\(\color{blue}{\text{ principal } + \text{ interest }}\)) is: \(\color{blue}{A = P + I}\)

Using the Formula: Key Steps

Step 1 — Convert the Rate

Always convert the percent rate to a decimal before multiplying. For example, \(\color{blue}{5\% = 0.05}\).

Step 2 — Confirm the Time Unit

If time is given in months, convert to years by dividing by 12. If given in days, divide by 365.

Step 3 — Substitute and Multiply

• \(\color{blue}{I = 1000 \times 0.05 \times 3 = $150}\) (P = $1000, \(\color{blue}{r = 5}\)%, \(\color{blue}{t = 3}\) years)

Step-by-Step Summary

1. Identify P (principal), r (rate), and t (time in years).
2. Convert the percent rate to a decimal.
3. Multiply: \(\color{blue}{I = P \times r \times t}\).
4. If needed, find the total: \(\color{blue}{A = P + I}\).
5. To find P, r, or t from I, rearrange the formula algebraically.

Watch: The Simple Interest Formula

The Organic Chemistry Tutor explains the \(\color{blue}{I = \text{ PRT }}\) formula and solves several word problems:

Simple Interest – Worked Examples

Example 1: Find the simple interest on a $1,000 principal at 5% per year for 3 years. What is the total amount?

\(\color{blue}{I = 1000 \times 0.05 \times 3 = $150}\). Total: \(\color{blue}{A = $1,000 + $150 = $1,150}\).

Example 2: Find the simple interest on $2,500 at 4% for 2 years.

\(\color{blue}{I = 2500 \times 0.04 \times 2 = $200}\). Total: \(\color{blue}{A = $2,500 + $200 = $2,700}\).

Example 3: How long will it take $800 to earn $120 in interest at 5% per year?

Rearrange: \(\color{blue}{t = I \div (P \times r) = 120 \div (800 \times 0.05) = 120 \div 40 = 3 \text{ years }}\).

Example 4: At what annual rate must $1,200 be invested to earn $144 in 2 years?

Rearrange: \(\color{blue}{r = I \div (P \times t) = 144 \div (1200 \times 2) = 144 \div 2400 = 0.06 = 6\%}\).

More Practice: Calculating Simple & Compound Interest

Khan Academy explains how to calculate simple interest and compare it with compound interest:

Exercises for Simple Interest

Use \(\color{blue}{I = P \times r \times t}\) to solve each problem.

1. P = $500, \(\color{blue}{r = 3}\)%, \(\color{blue}{t = 4}\) years. Find I and the total amount.
2. P = $1,200, \(\color{blue}{r = 6}\)%, \(\color{blue}{t = 2}\) years. Find I and the total amount.
3. P = $800, \(\color{blue}{r = 5}\)%, \(\color{blue}{t = 3}\) years. Find I and the total amount.
4. P = $3,000, \(\color{blue}{r = 2}\)%, \(\color{blue}{t = 5}\) years. Find I and the total amount.
5. P = $750, \(\color{blue}{r = 8}\)%, \(\color{blue}{t = 1}\) year. Find I and the total amount.

Answers

1. I = \(\color{blue}{$60}\); Total = \(\color{blue}{$560}\)
2. I = \(\color{blue}{$144}\); Total = \(\color{blue}{$1,344}\)
3. I = \(\color{blue}{$120}\); Total = \(\color{blue}{$920}\)
4. I = \(\color{blue}{$300}\); Total = \(\color{blue}{$3,300}\)
5. I = \(\color{blue}{$60}\); Total = \(\color{blue}{$810}\)

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Frequently Asked Questions

What is the simple interest formula?

The simple interest formula is I = Prt, where P is the principal (starting amount), r is the yearly interest rate as a decimal, and t is the time in years. For $2,000 at 4% for 3 years, I = 2,000 × 0.04 × 3 = $240. The total amount is A = P + I, which here is $2,240.

What is simple interest in simple words?

Simple interest is extra money paid or earned only on the original amount you borrow or save, not on interest already added. If you save $500 at 3% simple interest, you earn $15 every year, no matter how long the money stays. After 4 years, that is 4 × 15 = $60 in interest, for a total of $560.

What is the difference between simple interest and compound interest?

Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus interest that has already built up. With $1,000 at 10% for 2 years, simple interest gives $200. Compounded yearly, you earn $100 the first year and $110 the second, for $210. Over long periods, compounding grows much faster.

How do you find the simple interest rate?

Rearrange the formula to r = I ÷ (Pt), then turn the decimal into a percent. If $1,500 earns $180 in interest over 2 years, r = 180 ÷ (1,500 × 2) = 180 ÷ 3,000 = 0.06, or 6% per year. Make sure the time is in years; 18 months is 1.5 years.

Is simple interest monthly or yearly?

Simple interest rates are usually stated as a yearly (annual) rate, so time in the formula I = Prt is measured in years. If a problem gives months, divide by 12 first. For $3,000 at 5% for 8 months, t = 8/12 = 2/3, so I = 3,000 × 0.05 × 2/3 = $100. Always match the time unit to the rate.

How do you calculate simple interest on a loan?

Multiply the amount borrowed by the yearly rate and the number of years. For a $5,000 loan at 6% simple interest for 3 years, I = 5,000 × 0.06 × 3 = $900, so you repay $5,900 in total. Real loans may calculate interest daily on the remaining balance, so check the loan terms for the exact method.

Related Topics

• Percent Problems
• Percent of Increase and Decrease
• Discount, Tax, and Tip
• Exponential Growth and Decay
• Proportional Ratios