Simple Interest Lesson: Learn How to Calculate Interest and Total Amount With Examples
Lesson Overview
- What Is Simple Interest?
- How to Calculate Total Amount (A) after Interest:
- How to Calculate Simple Interest (SI) from Total Amount:
- Simple Interest Calculation for Different Time Periods (in Months)
Simple Interest is a way to figure out how much extra money you earn or owe when you borrow or lend money. It's calculated using a formula that involves three things: the amount of money you start with, the interest rate, and the time period.
Simple Interest (SI) is different from Compound Interest (CI). In SI, interest is calculated only on the original principal throughout the entire period, resulting in a linear growth of the amount. In CI, interest is calculated on both the principal and the accumulated interest, causing the amount to grow exponentially over time.
Simple Interest vs. Compound Interest
| Feature | Simple Interest | Compound Interest |
| Interest Calculation | Interest is calculated only on the principal. | Interest is calculated on both the principal and the accumulated interest. |
| Principal | Interest is based only on the original principal amount. | Interest is based on the growing amount (principal + previous interest). |
| Growth | Linear growth (interest is constant over time). | Exponential growth (interest grows faster over time). |
| Rate of Interest | Interest rate is fixed and applied for the entire period. | Interest rate is compounded and can apply at different intervals (annually, quarterly, etc.). |
| Final Amount | Total amount = Principal + Simple Interest. | Total amount includes both Principal and Compound Interest. |
| Common Use | Used for short-term loans like personal loans, car loans. | Used for long-term loans, savings, and investments. |
What Is Simple Interest?
Simple Interest is a fixed amount of interest calculated on the original principal amount over a period of time, without compounding.
What Is the Formula for Simple Interest?
We use three main formulas primarily for calculating simple interest.
How to Calculate Simple Interest (SI):
The formula for calculating Simple Interest (SI) is:
SI = (P × R × T) / 100
where:
- SI stands for simple interest.
- P is the Principal (the initial amount of money),
- R is the Rate of Interest (usually expressed as a percentage per year),
- T is the Time period for which the interest is calculated (usually in years).
This simple interest formula gives the extra amount earned or owed over the specified time period.
| Term | What it Means | Example |
| Principal (p) | The starting amount of money you borrow or save. It doesn't change while we calculate interest. | Lily borrows $100 from the bank - that's her Principal. |
| Rate (R) | The percentage of extra money you will pay or earn. | If the rate is 5%, Lily will pay or earn 5% of her $100 every year. |
| Time (T) | How long you borrow or save the money. Time is usually measured in years or months. | If Lily borrows the money for 1 year, the time is 1 year. |
| Amount (A) | The total money you pay or receive. It's the Principal plus the interest. | If Lily borrows $100 and has to pay $10 in interest, the total amount is $110. |
Example:
Sophie wants to buy a new bicycle, and her grandmother gives her $500 to save for the next 3 years. The bank will pay her 6% interest each year on the money she keeps in her account. How much Simple Interest will she earn on her $500 in 3 years?
Given
Principal (P) = $500
Rate of Interest (R) = 6%
Time (T) = 3 years
Formula
SI = (P x R x T) / 100
Using our example:
- Multiply the Principal and the Rate: 500 (Principal) x 6 (Rate) = 3000
- Multiply the result by the Time: 3000 x 3 (Time) = 9000
- Divide the result by 100: 9000 / 100 = 90
Sophie will earn $90 in interest after 3 years
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How to Calculate Total Amount (A) after Interest:
The formula of calculating total amount is:
A = P + SI
Or equivalently
A = P x (1 + R + T)
Where:
- A is the Total Amount (the sum of the principal and interest).
- P is the Principal (the initial amount).
- SI is the Simple Interest (calculated from the previous formula).
- In the second form, we combine the principal and the interest in one formula.
Example
Sophie has saved up $500 in her bank account, and after 3 years, she earned $90 in interest. Now, she wants to know how much money she will have in total after 3 years.
Given:
- Principal P = 500
- Simple Interest SI = 90
Formula:
A = P + SI
A = 500 + 90 = 590
The Total Amount after 3 years is $590.
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How to Calculate Simple Interest (SI) from Total Amount:
The formula for calculating Simple Interest (SI) from the Total Amount (A) is:
SI = A − P
Where:
- SI stands for Simple Interest (the extra amount earned or owed).
- A is the Total Amount (the sum of the principal and interest at the end of the time period).
- P is the Principal (the initial amount of money).
Example
Sophie checked her bank account after 3 years and saw that she had $590. She remembers that she started with $500, and now she's curious: How much interest did she earn during those 3 years?
Given
Total Amount (A) = $590
Principal (P) = $500
Formula
SI = A - P
SI = 590 - 500 = 90
The Simple Interest earned is $90.
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Let's take another example to understand it better.
Tom borrows $1,500 from the bank at a 10% simple interest rate for one
year to start his lemonade stand.
After one year, he makes $1,800 by selling lemonade. Let's calculate how much interest he needs to pay the bank and what his total repayment will be.
Step 1: Calculate the Simple Interest
The formula for simple interest is:
Substitute the values:
So, the interest Tom owes is $150.
Step 2: Calculate the Total Amount to Pay Back
Now, Tom has to pay back the principal $1,500 plus the interest $150:
Total Payment = 1500 + 150 = 1650
Step 3: Calculate Tom's Profit
Tom earned $1,800 from his lemonade sales. After paying back the bank:
Profit = 1800 - 1650 = 150
Tom makes $150 profit.
Simple Interest Calculation for Different Time Periods (in Months)
The formula for Simple Interest when the time period is given in months is:
Where:
- P = Principal amount (the initial amount of money borrowed or invested)
- R = Rate of interest per year (in percentage)
- T = Time period in months
Key Points:
The denominator includes 12 because the rate R is annual, but the time T is in months, so we divide by 12 to adjust the calculation.
Example:
If you borrow $1,000 at an interest rate of 6% per year for 6 months:
So, the simple interest for 6 months would be $30.
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