Simple Interest & Compound Interest
SSC-CGL Exams
1. Introduction
Interest is the extra amount paid for using someone else's money. SSC CGL often tests your understanding of the difference between Simple Interest (SI) and Compound Interest (CI) — and how to apply short tricks when the time period changes (yearly, half-yearly, quarterly).
2. Basic Definitions
| Term | Meaning |
|---|---|
| Principal (P) | The original amount borrowed or invested |
| Rate (R) | Interest rate per annum (per year) |
| Time (T) | Time period of investment or borrowing |
| Amount (A) | Final value after interest is added |
3. Simple Interest (SI)
In Simple Interest, the interest is calculated on the original principal only throughout the time period.
S.I. = (P × R × T) / 100
Amount = P + S.I.
Example 1
Find SI on ₹5000 for 3 years at 10% per annum.
S.I. = (5000 × 10 × 3) / 100 = ₹1500
Amount = ₹6500
4. Compound Interest (CI)
In Compound Interest, interest is added to the principal every year (or half-year, etc.) — so the next year's interest is on the new amount.
A = P (1 + R/100)^T
C.I. = A - P
Example 2
Find CI on ₹5000 for 2 years at 10% p.a.
A = 5000 (1 + 10/100)^2 = 5000 × (1.1)^2 = 5000 × 1.21 = ₹6050
C.I. = 6050 - 5000 = ₹1050
5. Difference Between SI and CI
| Basis | Simple Interest | Compound Interest |
|---|---|---|
| Calculation | On original principal | On principal + accumulated interest |
| Growth | Linear | Exponential |
| Formula | (P × R × T) / 100 | P(1 + R/100)^T - P |
| Value | Less | Greater |
| Used In | Loans, short-term payments | Banks, long-term deposits |
6. Difference Between SI and CI (Short Trick Formula)
For 2 years
Difference = P × (R/100)^2
For 3 years
Difference = P × (R/100)^2 × (3 + R)/100
Example 3
Find the difference between CI and SI on ₹5000 for 2 years at 10%.
= 5000 × (10/100)^2 = 5000 × 0.01 = ₹50
Difference = ₹50
Example 4
Find the difference between CI and SI on ₹4000 for 3 years at 10%.
= 4000 × (10/100)^2 × (3 + 10)/100
= 4000 × 0.01 × 0.13 = ₹52
Difference = ₹52
7. Compounding Periods
When interest is compounded more than once a year, rate and time are adjusted.
| Type | Rate Used | Time Used |
|---|---|---|
| Half-Yearly | R/2 | 2T |
| Quarterly | R/4 | 4T |
Example 5 (Half-Yearly Compounding)
Find CI on ₹8000 for 1 year at 10% p.a. compounded half-yearly.
R/2 = 5, T×2 = 2
A = 8000(1 + 5/100)^2 = 8000 × 1.1025 = ₹8820
CI = ₹820
Example 6 (Quarterly Compounding)
Find CI on ₹16000 for 1 year at 8% p.a., compounded quarterly.
R/4 = 2, T×4 = 4
A = 16000(1 + 2/100)^4 = 16000 × 1.0824 = ₹17318.4
CI = ₹1318.4
8. Shortcut Tricks
| Case | Shortcut Formula |
|---|---|
| SI | (P × R × T) / 100 |
| CI (annual) | P[(1 + R/100)^T - 1] |
| CI (half-yearly) | P[(1 + R/200)^2T - 1] |
| CI (quarterly) | P[(1 + R/400)^4T - 1] |
| Difference (2 years) | P(R/100)^2 |
| Difference (3 years) | P(R/100)^2 × (3 + R)/100 |
9. Practice Set
Q1. Find SI on ₹12000 for 2 years at 8% p.a.
View Answer
S.I. = (12000 × 8 × 2) / 100 = ₹1920
S.I. = ₹1920
Q2. Find CI on ₹10000 for 2 years at 10% per annum.
View Answer
A = 10000(1 + 0.10)^2 = 10000 × 1.21 = 12100
C.I. = 2100
CI = ₹2100
Q3. Find the difference between SI and CI on ₹5000 for 2 years at 12%.
View Answer
= 5000 × (12/100)^2 = 5000 × 0.0144 = ₹72
Difference = ₹72
Q4. Find CI on ₹16000 for 1.5 years at 10% p.a., compounded half-yearly.
View Answer
R/2 = 5%, T×2 = 3
A = 16000(1.05)^3 = 16000 × 1.157625 = ₹18522
CI = ₹2522
Q5. The difference between CI and SI on ₹25000 for 2 years is ₹50. Find the rate of interest.
View Answer
P(R/100)^2 = 50 ⇒ (R/100)^2 = 50/25000 = 1/500
R^2 = 20 ⇒ R = 4.47%
Rate ≈ 4.5%
Q6. Find CI on ₹10000 for 1 year at 12% per annum compounded quarterly.
View Answer
R/4 = 3%, T×4 = 4
A = 10000(1.03)^4 = 10000 × 1.1255 = ₹11255
CI = ₹1255
10. Quick Summary Table
| Concept | Formula | Notes |
|---|---|---|
| SI | (P × R × T) / 100 | Linear increase |
| CI | P(1 + R/100)^T - P | Compounded increase |
| Difference (2 yrs) | P(R/100)^2 | Quick trick |
| Half-Yearly CI | P(1 + R/200)^2T - P | R/2, 2T |
| Quarterly CI | P(1 + R/400)^4T - P | R/4, 4T |
You've completed Article 4: Simple Interest & Compound Interest!
Courage Tip: Always check if the question mentions "compounded annually," "half-yearly," or "quarterly." That single keyword changes the entire calculation — and your speed is your biggest weapon!
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