Simple Interest
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Important Formulas & Concepts
Study MaterialSimple Interest
Simple Interest is one of the most fundamental and important chapters in Quantitative Aptitude. Questions from this topic are frequently asked in SSC, Banking, Railway, CDS, NDA, UPSC, Defence, CAT, and placement examinations.
This chapter mainly deals with:
- Principal amount
- Rate of interest
- Time period
- Interest calculation
- Total amount
- Investment and borrowing concepts
Simple Interest is easy to understand because interest is always calculated only on the original principal amount.
What is Interest?
When a person borrows money from another person or bank, an extra amount paid for using that money is called interest.
Interest = Extra money paid on borrowed money
Example:
A borrows Rs. 1000 and returns Rs. 1100 after one year.
Interest:
= 1100 − 1000
= Rs. 100
Important Terminologies
1. Principal (P)
The original sum of money borrowed or invested is called principal.
Principal = Original Amount
2. Interest (I)
The extra amount paid for using borrowed money is called interest.
3. Amount (A)
The total money paid after adding interest to principal is called amount.
Amount = Principal + Interest
4. Rate of Interest (R)
The percentage charged on principal per year is called rate of interest.
It is usually expressed:
- Per annum (per year)
- In percentage (%)
5. Time (T)
The duration for which money is borrowed or invested is called time.
What is Simple Interest?
If interest is calculated only on the original principal throughout the entire period, it is called Simple Interest.
Simple Interest remains constant every year.
Basic Formula of Simple Interest
Let:
- Principal = P
- Rate = R% per annum
- Time = T years
Then:
Simple Interest = (P × R × T) / 100
Formula for Amount
Total amount after interest:
Amount = Principal + Simple Interest
or
A = P + SI
Formula for Principal
If SI, Rate and Time are given:
Principal = (100 × SI) / (R × T)
Formula for Rate of Interest
If SI, Principal and Time are given:
Rate = (100 × SI) / (P × T)
Formula for Time
If SI, Principal and Rate are given:
Time = (100 × SI) / (P × R)
Important Formula Summary
| Concept | Formula |
|---|---|
| Simple Interest | (P × R × T)/100 |
| Amount | P + SI |
| Principal | (100 × SI)/(R × T) |
| Rate | (100 × SI)/(P × T) |
| Time | (100 × SI)/(P × R) |
Understanding the Concept of Simple Interest
In Simple Interest:
- Interest is calculated only on principal.
- Interest remains same every year.
- Interest does not increase over time.
Year-wise Interest Concept
| Year | Interest |
|---|---|
| 1st Year | Same |
| 2nd Year | Same |
| 3rd Year | Same |
✔ In Simple Interest, yearly interest always remains constant.
Simple Interest vs Compound Interest
| Simple Interest | Compound Interest |
|---|---|
| Calculated on principal only | Calculated on principal + previous interest |
| Interest remains constant | Interest increases every year |
| Easy calculations | Comparatively complex calculations |
Direct Amount Formula
Instead of calculating SI separately:
Amount = P (1 + RT/100)
Concept of Annual Increase
Simple Interest increases linearly with time.
If:
- Time doubles → Interest doubles
- Rate doubles → Interest doubles
- Principal doubles → Interest doubles
Important Observations
1. SI is Directly Proportional
Simple Interest is directly proportional to:
- Principal
- Rate
- Time
2. Interest for Equal Time
✔ For equal time periods, SI ratio equals principal ratio.
3. Interest Remains Fixed
✔ Same principal and same rate produce equal yearly interest.
Common Mistakes in Simple Interest
- Using Compound Interest formula accidentally.
- Incorrect percentage conversion.
- Ignoring time unit conversion.
- Calculation mistakes in amount formula.
- Confusing principal with amount.
Important Exam Tips
- Memorize all SI formulas.
- Convert months into years carefully.
- Use direct amount formula for faster solving.
- Read whether rate is annual or monthly.
- Practice ratio-based SI questions regularly.
- Verify percentage calculations properly.
- Differentiate SI and CI clearly.
Quick Revision Table
| Required Quantity | Formula |
|---|---|
| Simple Interest | (P×R×T)/100 |
| Amount | P+SI |
| Principal | (100×SI)/(RT) |
| Rate | (100×SI)/(PT) |
| Time | (100×SI)/(PR) |
Simple Interest is one of the easiest and most scoring chapters in Quantitative Aptitude. Strong understanding of formulas, percentage calculations, and time-based concepts helps candidates solve questions quickly and accurately in competitive examinations.