Whenever you borrow money or park it in a savings product, interest is the price of using that money. It is the extra amount the borrower pays, or the reward the saver earns. There are two main ways interest is calculated: simple interest and compound interest. Simple interest is the easier of the two, and understanding it is the first step toward understanding loans, deposits and investments.
This guide explains the simple interest formula in plain language. You will learn how to calculate interest for years, months and days, how to work out the rate, the time or the principal, how it differs from compound interest, and where it is used in the real world. There are plenty of worked examples, a list of common mistakes and practice questions. To check any calculation quickly, use our free simple interest calculator.
Quick Answer: The Simple Interest Formula
Simple Interest (SI) = (P × R × T) ÷ 100
- P = principal (the amount borrowed or invested)
- R = annual interest rate in percent
- T = time in years
Total amount = P + SI. Example: 25,000 at 8% for 3 years gives SI = (25,000 × 8 × 3) ÷ 100 = 6,000, so the total is 31,000.
What Is Interest?
Interest is the cost of borrowing money or the income earned from lending or saving it. If you deposit money in a bank, the bank uses it and pays you interest. If you take a loan, you pay interest to the lender on top of returning the amount you borrowed.
Three ingredients determine how much interest is charged:
- Principal (P): the original sum of money.
- Rate (R): the percentage charged per year, often written “per annum” or “p.a.”.
- Time (T): how long the money is borrowed or invested.
The bigger any of these three, the larger the interest. If the rate is a percentage, it helps to be comfortable with percentages first. Our guide on how to calculate percentage covers the basics you need.
The Simple Interest Formula
Simple interest is calculated only on the original principal. The interest earned each period is the same and does not grow, because previous interest is never added to the base.
SI = (P × R × T) ÷ 100
Why divide by 100? Because the rate R is expressed as a percent, and a percent means “per hundred”. So 8% means 8 ÷ 100 = 0.08. You could also write the formula as SI = P × (R ÷ 100) × T.
Once you have the interest, the total amount to be repaid or received is:
Amount (A) = P + SI = P × (1 + (R × T) ÷ 100)
Step-by-Step Calculation
Steps
- Write down P, R and T. Make sure T is in years and R is the annual rate.
- Multiply P × R × T.
- Divide the result by 100 to get the interest.
- Add the interest to the principal if you need the total amount.
Example 1: Fixed Deposit
You deposit 10,000 at 7% simple interest for 1 year. SI = (10,000 × 7 × 1) ÷ 100 = 700. Total = 10,700.
Example 2: Multi-Year Loan
You borrow 25,000 at 8% per year for 3 years. SI = (25,000 × 8 × 3) ÷ 100 = 600,000 ÷ 100 = 6,000. Total repayment = 25,000 + 6,000 = 31,000.
Example 3: Personal Loan Between Friends
12,000 is lent at 5% for 4 years. SI = (12,000 × 5 × 4) ÷ 100 = 2,400. Total = 14,400.
Notice how the interest grows in a straight line. Doubling the time doubles the interest, and doubling the rate also doubles it. This is called linear growth.
Handling Months and Days
The formula needs time in years. When the period is shorter than a year, convert it first.
Months to Years
T = Months ÷ 12
Example: 50,000 at 6% for 9 months. T = 9 ÷ 12 = 0.75. SI = (50,000 × 6 × 0.75) ÷ 100 = 225,000 ÷ 100 = 2,250.
Days to Years
T = Days ÷ 365 (some lenders use 360 days; check your agreement)
Example: 20,000 at 9% for 73 days. T = 73 ÷ 365 = 0.2. SI = (20,000 × 9 × 0.2) ÷ 100 = 360.
Half-Year Example
15,000 at 8% for 6 months. T = 0.5. SI = (15,000 × 8 × 0.5) ÷ 100 = 600.
| Period | T in years |
|---|---|
| 3 months | 0.25 |
| 6 months | 0.5 |
| 9 months | 0.75 |
| 18 months | 1.5 |
| 73 days | 0.2 (73 ÷ 365) |
| 146 days | 0.4 (146 ÷ 365) |
Finding Rate, Time or Principal
The simple interest formula can be rearranged to find any missing value, provided you know the other three.
| To find | Formula |
|---|---|
| Interest (SI) | (P × R × T) ÷ 100 |
| Principal (P) | (SI × 100) ÷ (R × T) |
| Rate (R) | (SI × 100) ÷ (P × T) |
| Time (T) | (SI × 100) ÷ (P × R) |
Finding the Rate
A loan of 6,000 earns 1,800 interest in 3 years. R = (1,800 × 100) ÷ (6,000 × 3) = 180,000 ÷ 18,000 = 10% per year.
Finding the Time
8,000 earns 2,400 interest at 6%. T = (2,400 × 100) ÷ (8,000 × 6) = 240,000 ÷ 48,000 = 5 years.
Finding the Principal
Interest of 1,500 is earned at 5% over 2 years. P = (1,500 × 100) ÷ (5 × 2) = 150,000 ÷ 10 = 15,000.
Finding the Rate from Amounts
7,500 grows to 9,000 in 4 years. The interest is 9,000 − 7,500 = 1,500. R = (1,500 × 100) ÷ (7,500 × 4) = 150,000 ÷ 30,000 = 5%.
Doubling Time
With simple interest, money doubles when the interest equals the principal. That means R × T = 100. At 10% simple interest, money doubles in 10 years; at 5%, in 20 years. This differs from compound interest, where the doubling time is much shorter, as explained in our compound interest guide.
Year-by-Year Growth
Here is how 10,000 grows at 8% simple interest. The interest added each year is a constant 800.
| Year | Interest for the year | Total interest so far | Amount |
|---|---|---|---|
| 1 | 800 | 800 | 10,800 |
| 2 | 800 | 1,600 | 11,600 |
| 3 | 800 | 2,400 | 12,400 |
| 4 | 800 | 3,200 | 13,200 |
| 5 | 800 | 4,000 | 14,000 |
Simple Interest vs Compound Interest
The big difference is what the interest is calculated on. Simple interest uses only the original principal. Compound interest uses the principal plus all interest already earned, so you earn interest on interest.
Example: Take 10,000 at 8% for 5 years.
- Simple interest: SI = (10,000 × 8 × 5) ÷ 100 = 4,000. Amount = 14,000.
- Compound interest (yearly): Amount = 10,000 × 1.08⁵ = 10,000 × 1.469328 = 14,693.28. Interest = 4,693.28.
The difference is 693.28 after only five years, and it widens quickly over longer periods. Another example: 20,000 at 10% for 2 years gives simple interest of 4,000 but compound interest of 20,000 × 1.21 − 20,000 = 4,200.
| Feature | Simple interest | Compound interest |
|---|---|---|
| Calculated on | Original principal only | Principal plus accumulated interest |
| Growth pattern | Linear (straight line) | Exponential (curved upward) |
| Formula | P × R × T ÷ 100 | P × (1 + r)ⁿ − P |
| Better for savers | No | Yes |
| Better for borrowers | Usually yes | Usually no |
Where Is Simple Interest Used?
Short-Term Loans and Personal Lending
Informal loans between individuals, short-term business credit and some consumer loans use simple interest because it is easy to understand and calculate.
Some Car and Education Loans
A number of auto loans in several countries are calculated using simple interest on the outstanding balance. In that setup, paying early reduces the interest you owe. Always read your loan agreement to confirm the method.
Bonds and Treasury Bills
Many bonds pay a fixed coupon, which is a form of simple interest on the face value. Treasury bills and some short-term government securities are also priced using simple interest conventions.
Late Payment Charges and Penalties
Overdue invoices, tax dues and utility bills often carry simple interest for each day or month of delay.
Savings Certificates and Short Deposits
Some short deposits pay simple interest at maturity, especially if the term is under a year.
Education and Everyday Money Decisions
Simple interest is the building block for learning how loans and savings work. After it, you can move on to compound interest, how EMI is calculated and SIP investing.
Note: Whether a particular product uses simple or compound interest depends on the lender and on local rules. Always check the terms before signing.
Monthly Rates vs Annual Rates
Informal lenders often quote a rate per month, such as “2% per month”. The formula expects an annual rate, so convert it: 2% per month = 24% per year. On a loan of 10,000, that is 2,400 per year, or 200 per month.
The reverse is also true. If a bank quotes 9% per annum and you want the monthly rate for simple interest, divide by 12 to get 0.75% per month. Always check whether a rate is “per annum” or “per month” before calculating. Mixing them up is one of the most expensive mistakes borrowers make.
Practical Tips for Borrowers and Savers
- Compare total cost, not just the rate. A lower rate on a longer loan can cost more in total interest.
- Ask whether the interest is simple or compound. A quoted rate means different things depending on the method.
- Check for fees. Processing charges and insurance can add to the real cost of a loan.
- Pay early where allowed. With simple interest on a reducing balance, early payments cut your interest bill.
- Compare with inflation. If prices rise faster than your interest, your savings lose buying power. See our guide on how inflation is calculated.
- Judge returns properly. Our article on how to calculate ROI shows how to compare options fairly.
This information is for education and is not financial advice. For decisions involving large sums, consult a qualified financial professional.
Common Mistakes
- Not converting time to years. Using 9 for nine months instead of 0.75 gives an answer 12 times too large.
- Using a monthly rate as if it were annual. Convert 2% per month into 24% per year first.
- Forgetting to divide by 100. Multiplying P × R × T and stopping gives a number 100 times too big.
- Using the formula for compound products. If interest is added to the principal periodically, simple interest underestimates the result.
- Confusing interest with total amount. SI is only the interest; the total includes the principal.
- Mixing 360 and 365 day years without checking the lender’s convention.
- Entering R as 0.08 and still dividing by 100. Use R = 8 with ÷ 100, or R = 0.08 without ÷ 100, but not both.
Practice Questions
- Find the simple interest and total amount on 12,000 at 5% for 4 years.
- Find the simple interest on 15,000 at 8% for 6 months.
- In how many years will 5,000 earn 900 interest at 6%?
- 7,500 becomes 9,000 in 4 years at simple interest. What is the rate?
- The simple interest on a sum at 7% for 3 years is 1,260. Find the principal.
- Compare simple and compound (yearly) interest on 20,000 at 10% for 2 years.
Answers
- SI = 2,400; total = 14,400.
- SI = (15,000 × 8 × 0.5) ÷ 100 = 600.
- T = (900 × 100) ÷ (5,000 × 6) = 3 years.
- SI = 1,500; R = (1,500 × 100) ÷ (7,500 × 4) = 5%.
- P = (1,260 × 100) ÷ (7 × 3) = 126,000 ÷ 21 = 6,000.
- Simple interest = 4,000; compound interest = 20,000 × 1.21 − 20,000 = 4,200.
Frequently Asked Questions
What is the simple interest formula?
SI = (P × R × T) ÷ 100, where P is the principal, R is the annual rate in percent and T is the time in years.
How do I calculate the total amount with simple interest?
Add the interest to the principal: A = P + SI, or equivalently A = P × (1 + RT ÷ 100).
How do I calculate simple interest for months?
Divide the number of months by 12 to get years. Nine months is 0.75 years.
How do I calculate simple interest for days?
Divide the days by 365, or by 360 if your lender uses that convention.
What is the difference between simple and compound interest?
Simple interest is based only on the original principal, while compound interest is based on principal plus previously earned interest, so it grows faster.
How do I find the rate in simple interest?
Use R = (SI × 100) ÷ (P × T).
Is simple interest better for borrowers?
Generally yes, because it usually costs less than compound interest at the same rate over the same period.
Conclusion
The simple interest formula, SI = (P × R × T) ÷ 100, is straightforward but powerful. Keep time in years, use the annual rate, remember to divide by 100, and add the interest to the principal for the total amount. You can rearrange the formula to find the rate, time or principal, and you can compare it with compound interest to see why saving early and long can make such a difference.
For quick, accurate answers, use our free simple interest calculator, and continue learning with these related guides: