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.
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
- Identify P (principal), r (rate), and t (time in years).
- Convert the percent rate to a decimal.
- Multiply: \(\color{blue}{I = P \times r \times t}\).
- If needed, find the total: \(\color{blue}{A = P + I}\).
- 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.
- P = $500, \(\color{blue}{r = 3}\)%, \(\color{blue}{t = 4}\) years. Find I and the total amount.
- P = $1,200, \(\color{blue}{r = 6}\)%, \(\color{blue}{t = 2}\) years. Find I and the total amount.
- P = $800, \(\color{blue}{r = 5}\)%, \(\color{blue}{t = 3}\) years. Find I and the total amount.
- P = $3,000, \(\color{blue}{r = 2}\)%, \(\color{blue}{t = 5}\) years. Find I and the total amount.
- P = $750, \(\color{blue}{r = 8}\)%, \(\color{blue}{t = 1}\) year. Find I and the total amount.
Answers
- I = \(\color{blue}{$60}\); Total = \(\color{blue}{$560}\)
- I = \(\color{blue}{$144}\); Total = \(\color{blue}{$1,344}\)
- I = \(\color{blue}{$120}\); Total = \(\color{blue}{$920}\)
- I = \(\color{blue}{$300}\); Total = \(\color{blue}{$3,300}\)
- I = \(\color{blue}{$60}\); Total = \(\color{blue}{$810}\)
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus previously earned interest, causing the balance to grow faster over time.
How do I convert months to years for the time variable?
Divide the number of months by 12. For example, 6 months = \(\color{blue}{\frac{6}{12} = 0.5}\) years.
Can I rearrange \(\color{blue}{I = \text{ PRT }}\) to find the rate or principal?
Yes. \(\color{blue}{P = I \div (r \times t)}\), \(\color{blue}{r = I \div (P \times t)}\), and \(\color{blue}{t = I \div (P \times r)}\). Simply divide both sides of the formula by whatever is multiplied with the unknown.
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