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.
A person invests ₹12,000 at 7.5% simple interest per annum. How much total amount will he receive after 2.5 years?
Practice 2easy
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 3easy
At what rate of simple interest per annum will ₹2,400 amount to ₹3,120 in 5 years?
Practice 4easy
A principal of ₹8,000 earns ₹1,600 as simple interest in 4 years. What is the rate of interest per annum?
Practice 5easy
In how many years will ₹6,000 become ₹7,800 at a simple interest rate of 6% per annum?
Practice 6medium
Priya lent ₹20,000 to Raj at 5% per annum simple interest for 3 years. After 3 years, Raj returned the amount with interest. Priya then invested this entire amount at 8% per annum simple interest for 2 years. What is the total interest earned by Priya over the entire period?
Practice 7medium
A sum of money becomes ₹8,400 after 5 years at a simple interest rate of 8% per annum. What was the principal amount?
Practice 8medium
Rahul borrowed ₹12,000 at 9% per annum simple interest. After how many years will the total amount (principal + interest) become ₹16,320?
Practice 9medium
A person invests ₹15,000 at 10% per annum simple interest. How much additional principal must be invested at 12% per annum to make the average rate of interest 11% per annum?
Practice 10medium
A sum of ₹8,000 is divided into two parts. One part is invested at 6% per annum and the other at 9% per annum simple interest. If the total interest earned in 2 years is ₹1,200, what is the amount invested at 9% per annum?
Practice 11hard
A sum of money becomes ₹5,400 in 3 years and ₹6,480 in 5 years at simple interest. What is the principal amount?
Practice 12hard
Rajesh borrowed ₹8,000 at a simple interest rate of 12% per annum. After some time, he repaid ₹10,240. If he had borrowed the same amount at 15% per annum for the same period, how much more interest would he have paid?
Practice 13hard
A person invests ₹15,000 at 10% per annum simple interest. Every year, he withdraws ₹1,500 (principal + interest combined). After how many complete years will his investment reduce to zero or below?
Practice 14hard
Arun borrowed ₹20,000 at 9% per annum simple interest from a bank. He repaid ₹8,000 after 1 year and ₹8,000 after 2 years. How much does he still owe at the end of 3 years?
Practice 15hard
Two sums of money are in the ratio 4:5. They are lent at simple interest rates of 5% and 4% per annum respectively. After 4 years, the difference in the interests earned is ₹160. What is the larger sum?
Practice 16hard
Priya lent ₹12,000 to Neha at 8% per annum simple interest. After 2 years, Neha returned ₹14,000 and the remaining amount after 1 more year. What amount did Neha return in the 3rd year?
60-Second Revision — Simple Interest
Formula: SI = (P × R × T) / 100, Amount = P + SI
Remember: Always match time units with rate units before calculation
Shortcut: 10% rate means SI = Principal × Time ÷ 10
Trap: Never add interest multiple times in simple interest
Quick check: If money doubles in t years, rate = 100/t percent
Inverse relation: Rate doubles, time halves for same SI
Convert months to years by dividing by 12 when rate is per annum