Simple Interest
Learn how to calculate interest earned on savings or owed on loans using the simple interest formula.
Definition
The Simple Interest Formula
- = Interest (the amount earned or owed)
- = Principal (the starting amount)
- = Rate (annual interest rate as a decimal)
- = Time (in years)
Finding the Total Amount
Try it now
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?
Identify the values
, , → Values identified
Write the formula
→ Formula ready
Substitute the values
→ Values substituted
Calculate step by step
, then →
Answer: You will earn 60 dollars in interest after 3 years.
Common Mistakes
Forgetting to convert percentage to decimal
Why it's wrong: Using instead of gives an answer 100 times too large.
Correct: Always divide the percentage by 100:
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 = years
Confusing interest with total amount
Why it's wrong: Interest () is just what you earn/owe. Total amount () includes the principal.
Correct: Total amount = Principal + Interest:
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
17 problemsIn the simple interest formula , what does represent?
Why It Matters
- 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: Credit cards and personal loans often start with simple interest concepts
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 dollars.
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 :
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 dollars in interest.
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 dollars.
Key Takeaways
- 1Simple interest formula:
- 2Always convert percentage rate to decimal (divide by 100)
- 3Time must be in years (convert months by dividing by 12)
- 4Total amount = Principal + Interest:
- 5Simple interest is calculated only on the original principal, not on accumulated interest
Frequently Asked Questions
Glossary
- Principal
- The original amount of money deposited or borrowed (symbol: )
- Interest
- The fee paid for borrowing money, or earned on savings (symbol: )
- Interest Rate
- The percentage of principal charged or earned per time period (symbol: )
- 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