Core ConceptRead this first — the foundation of the topic
Simple Interest is the extra money paid on borrowed money or earned on invested money. It is calculated only on the original amount (called Principal) for a specific time period at a fixed rate. Core Concept: Simple Interest remains constant every year. If you borrow Rs. 1000 at 10% simple interest, you pay Rs. 100 every year as interest. The principal amount never changes in calculations.
Formula BlockMemorise — at least one formula appears in every paper
Block:
Simple Interest (SI) = (P × R × T) / 100
Amount = Principal + Simple Interest
Principal (P) = (SI × 100) / (R × T)
Rate (R) = (SI × 100) / (P × T)
Time (T) = (SI × 100) / (P × R)
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL consistently asks 2-3 questions on Simple Interest. Common question types include finding SI when P, R, T are given, calculating time or rate when other values are known, and comparing simple vs compound interest scenarios.
Master Shortcut #1 - Quick SI Calculation:
For easy percentages, use direct multiplication:
- 10% of any amount = Amount/10
- 5% of any amount = Amount/20
- 20% of any amount = Amount/5
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Identify P = 8000, R = 12%, T = 3 years
2
Step 2
Apply formula SI = (P × R × T) / 100
3
Step 3
SI = (8000 × 12 × 3) / 100
4
Step 4
SI = 288000 / 100 = Rs. 2880
5
Step 5
Amount = 8000 + 2880 = Rs. 10,880
Shortcut #2 - Time-Rate Relationship:
If rate doubles, time becomes half for same SI.
If time doubles, rate becomes half for same SI.
This helps eliminate wrong options quickly.
Worked Example 2:
Question: At what rate will Rs. 5000 amount to Rs. 6500 in 4 years at simple interest?
1
Step 1
Amount = 6500, Principal = 5000
2
Step 2
SI = Amount - Principal = 6500 - 5000 = Rs. 1500
3
Step 3
Using R = (SI × 100) / (P × T)
4
Step 4
R = (1500 × 100) / (5000 × 4)
5
Step 5
R = 150000 / 20000 = 7.5%
Shortcut #3 - Percentage Method:
When principal becomes 'n' times in 't' years:
Rate = [(n-1) × 100] / t
Example: If money doubles (n=2) in 10 years, Rate = (2-1) × 100/10 = 10%
Most Common Trap: Students often confuse the time unit. If rate is per annum but time is given in months, convert months to years by dividing by 12. Always match the time unit with the rate unit. This single mistake costs many marks in SSC CGL.
Another frequent error is adding interest multiple times. Remember, in simple interest, you add interest only once to get the final amount, unlike compound interest where interest compounds.
Key Points to Remember
Simple Interest formula: SI = (P × R × T) / 100 where P=Principal, R=Rate, T=Time
Amount = Principal + Simple Interest (add only once, not yearly)
SI remains constant every year unlike compound interest which grows
Quick calculation: 10% SI = Principal/10, 20% SI = Principal/5
If money becomes n times in t years, Rate = [(n-1) × 100] / t
Time and rate are inversely proportional for same SI amount
Always convert time units to match rate units (months to years or vice versa)
Principal can be found using: P = (SI × 100) / (R × T)
Rate doubles means time halves for same SI amount earned
Common trap: Never compound the interest in simple interest problems
Exam-Specific Tips
Standard SI formula uses division by 100, never by 1000 or other numbers
When rate is given per annum, time must be in years for direct calculation
If principal doubles, the rate-time product always equals 100
SI for 2 years at 10% rate equals 20% of principal amount
Principal formula derivation: P = (SI × 100) / (R × T)
Rate formula: R = (SI × 100) / (P × T) gives percentage value
Time formula: T = (SI × 100) / (P × R) gives time in rate's unit
Amount formula: A = P + SI = P[1 + (R × T)/100]
Practice MCQs
Simple Interest — Practice Questions
26graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 26
Rahul borrowed ₹12,000 at 5% simple interest per annum. If he paid ₹1,800 as interest, for how many years did he borrow the money?
Practice 2easy
Priya invested ₹20,000 at 6% simple interest per annum. How much amount will she have after 5 years?
Practice 3easy
A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned after 3 years?
Practice 4easy
A principal of ₹15,000 earns ₹4,500 as simple interest in 6 years. What is the rate of interest per annum?
Practice 5easy
A principal amount earns ₹2,400 as simple interest at 6% per annum in 4 years. What is the principal amount?
Practice 6easy
If ₹15,000 becomes ₹18,600 in 3 years under simple interest, what is the rate of interest per annum?
Practice 7easy
A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the total amount after 3 years?
Practice 8easy
Rahul borrowed ₹12,000 at 5% simple interest per annum. If he paid ₹2,400 as interest, for how many years did he borrow the money?
Practice 9easy
At what rate of simple interest per annum will ₹8,000 amount to ₹10,400 in 4 years?
Practice 10medium
A principal amount doubles itself in 10 years at simple interest. At the same rate of interest, in how many years will it become 4 times the original principal?
Practice 11medium
Rahul borrowed ₹12,000 at 8% per annum simple interest. After how many years will the interest amount be equal to half the principal?
Practice 12medium
A person borrowed ₹12,000 at 9% per annum simple interest. After how many years will the total amount (principal + interest) become ₹17,400?
Practice 13medium
A sum of ₹5,000 is invested at simple interest. If the rate of interest is increased by 2% per annum, the interest earned in 3 years increases by ₹300. If the original interest earned in 3 years was ₹900, what is the original rate of interest?
Practice 14medium
A certain sum of money is lent at simple interest. The ratio of the sum and the simple interest earned in 4 years is 5 : 2. What is the rate of interest per annum?
Practice 15medium
A sum of money becomes ₹8,400 after 4 years at a simple interest rate of 5% per annum. What was the principal amount?
Practice 16medium
Two amounts are invested at simple interest: ₹5,000 at 6% p.a. for 3 years, and ₹8,000 at 5% p.a. for 2 years. What is the total interest earned from both investments?
Practice 17medium
A sum of money becomes ₹8,400 after 5 years at a simple interest rate of 8% per annum. What is the principal amount?
Practice 18medium
The simple interest on a certain sum for 3 years at 12% per annum is ₹2,160. What will be the simple interest on the same sum for 5 years at 10% per annum?
Practice 19medium
Two equal sums of money are lent at simple interest. The first sum is lent at 10% per annum for 4 years, and the second sum is lent at 8% per annum for 5 years. What is the ratio of the simple interests earned?
Practice 20hard
A lender charges simple interest at 12% p.a. A borrower takes ₹5,000 and after some time, the total amount (principal + interest) becomes ₹6,800. If the borrower had taken ₹7,500 at the same rate for the same period, what would be the total amount?
6 more practice questions in the Study Panel
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