Simple Interest

Learn how to calculate interest earned on savings or owed on loans using the simple interest formula.

Intermediate25 min17 problems
Practice Problems

Definition

Simple interest is money earned or paid on a principal amount at a fixed rate over time. Unlike compound interest, simple interest is calculated only on the original principal.

The Simple Interest Formula

I=P×r×tI = P \times r \times t
Where:
  • II = Interest (the amount earned or owed)
  • PP = Principal (the starting amount)
  • rr = Rate (annual interest rate as a decimal)
  • tt = Time (in years)

Finding the Total Amount

To find the total amount after interest:
A=P+IA = P + I
Or combined:
A=P(1+rt)A = P(1 + rt)

Try it now

In the simple interest formula I=P×r×tI = P \times r \times t, what does PP represent?

Worked Examples

You deposit 500 dollars in a savings account that pays 4% simple interest per year. How much interest will you earn after 3 years?
1

Identify the values

P=500P = 500, r=4%=0.04r = 4\% = 0.04, t=3t = 3 → Values identified
2

Write the formula

I=P×r×tI = P \times r \times t → Formula ready
3

Substitute the values

I=500×0.04×3I = 500 \times 0.04 \times 3 → Values substituted
4

Calculate step by step

I=500×0.04=20I = 500 \times 0.04 = 20, then 20×3=6020 \times 3 = 60 → I=60I = 60

Common Mistakes

Forgetting to convert percentage to decimal

Why it's wrong: Using r=5r = 5 instead of r=0.05r = 0.05 gives an answer 100 times too large.

Correct: Always divide the percentage by 100: 5%=5÷100=0.055\% = 5 \div 100 = 0.05

Using months instead of years for time

Why it's wrong: The formula uses annual rate, so time must be in years.

Correct: Convert months to years: 6 months = 612=0.5\frac{6}{12} = 0.5 years

Confusing interest with total amount

Why it's wrong: Interest (II) is just what you earn/owe. Total amount (AA) includes the principal.

Correct: Total amount = Principal + Interest: A=P+IA = P + I

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Formula
Simple Interest:I = P × r × t = 500 × 0.04 × 3 = $60.00

Simple Interest

Interest Earned:$60.00
Total Amount:$560.00

Growth Over Time

yearsAmount

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Practice Problems

17 problems
Problem 1 of 17
Easy
In the simple interest formula I=P×r×tI = P \times r \times t, what does PP represent?

Why It Matters

Understanding simple interest is essential for making smart financial decisions:
  • Savings accounts: Know how much your money will grow over time
  • Loans: Understand how much you will pay back on borrowed money
  • Investments: Compare different investment options
  • Car loans: Many auto loans use simple interest
  • Short-term borrowing: Short personal loans are often priced with simple interest
Learning this formula helps you evaluate financial products and plan for your future!

Real World Applications

Savings Account Growth

Banks pay you interest for keeping money in savings accounts. Simple interest shows the basic growth pattern.

Example:

A savings account with 800 dollars at 3% for 2 years earns 800×0.03×2=48800 \times 0.03 \times 2 = 48 dollars.

1Try It Yourself

You have 1200 dollars in a savings account that pays 5% simple interest per year.

How much interest will you earn in 2 years?

Step 1: Write the mathematical expression

Use the formula I=P×r×tI = P \times r \times t:

Car Loans

Many car loans use simple interest. Understanding this helps you know exactly how much extra you will pay.

Example:

A 10000 dollar car loan at 7% for 5 years means paying 10000×0.07×5=350010000 \times 0.07 \times 5 = 3500 dollars in interest.

2Try It Yourself

You take a car loan of 8000 dollars at 6% simple interest for 4 years.

What is the total amount you will pay back?

Step 1: Write the mathematical expression

First find interest, then add to principal:

Lending Money to Friends

Even informal loans can involve interest. Understanding simple interest helps both parties agree on fair terms.

Example:

If you lend 200 dollars to a friend at 2% for 6 months, the interest is 200×0.02×0.5=2200 \times 0.02 \times 0.5 = 2 dollars.

Key Takeaways

  • 1Simple interest formula: I=P×r×tI = P \times r \times t
  • 2Always convert percentage rate to decimal (divide by 100)
  • 3Time must be in years (convert months by dividing by 12)
  • 4Total amount = Principal + Interest: A=P+IA = P + I
  • 5Simple interest is calculated only on the original principal, not on accumulated interest

Frequently Asked Questions

Simple interest is calculated only on the original principal. Compound interest is calculated on the principal PLUS any interest already earned, so it grows faster over time.
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal PLUS any interest already earned, so it grows faster over time.
Percentages are a way to express parts per hundred. To use them in calculations, we convert to decimals: 5%=5100=0.055\% = \frac{5}{100} = 0.05. This ensures the math works correctly.
Yes! Convert months to years by dividing by 12. For example, 6 months = 0.5 years, 3 months = 0.25 years.

Glossary

Principal
The original amount of money deposited or borrowed (symbol: PP)
Interest
The fee paid for borrowing money, or earned on savings (symbol: II)
Interest Rate
The percentage of principal charged or earned per time period (symbol: rr)
Simple Interest
Interest calculated only on the original principal, not on accumulated interest
Annual
Per year; simple interest rates are usually given as annual percentages
Today's challengeOne problem, three tries

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