Compound Interest – All Formulas, Tricks, and Examples
Compound Interest – Formula, Tricks, and Examples
Compound Interest is one of the most important chapters in Quantitative Aptitude. Questions from this topic are frequently asked in exams such as SSC, Banking, Railway, CAT, MBA entrance exams, and placement tests.
If students clearly understand the formulas, growth pattern, and shortcuts of Compound Interest, they can solve questions faster and more accurately in competitive exams.
Quick Summary
Compound Interest
Interest is calculated on both the principal and the previous interest.
Main Formula
A = P(1 + R/100) T
Exam Use
Common in banking, finance, growth, depreciation, and population-based problems.
What is Compound Interest?
Definition
Compound Interest (CI) is the interest calculated not only on the original Principal (P), but also on the interest added in previous periods.
In simple words, interest keeps getting added to the amount, and next time interest is calculated on the new total amount.
Why is it called Compound Interest?
Because the interest is compounded, which means it is repeatedly added to the principal, and the next interest is calculated on the increased amount.
Important Terms in Compound Interest
| Term | Meaning |
|---|---|
| Principal (P) | Original money invested or borrowed. |
| Rate (R) | Rate of interest per annum. |
| Time (T) | Total time period for which money is invested or borrowed. |
| Amount (A) | Final amount after adding compound interest. |
| Compound Interest (CI) | Interest earned after compounding over time. |
Compound Interest Formulas
1. Amount Formula
A = P(1 + R/100) T
This is the most important compound interest formula. It gives the final amount after T years.
2. Compound Interest Formula
CI = A - P
First find the amount, then subtract the principal to get compound interest.
3. Direct CI Formula
CI = P[(1 + R/100) T - 1]
This formula directly gives compound interest without separately finding amount.
4. Half-Yearly Compound Interest
A = P(1 + R/200) 2T
When interest is compounded every 6 months, rate becomes half and time becomes double.
5. Quarterly Compound Interest
A = P(1 + R/400) 4T
When interest is compounded quarterly, rate becomes one-fourth and time becomes four times.
6. If Rates are Different for Different Years
A = P(1 + r1/100)(1 + r2/100)(1 + r3/100)...
Use this formula when the rate of interest changes every year.
7. Population / Growth Formula
Final Value = Initial Value(1 + R/100) T
Same formula is used in population growth, production increase, and investment growth.
8. Depreciation Formula
Final Value = Initial Value(1 - R/100) T
Used when the value of an item decreases every year, such as machine value or car value.
9. Difference Between CI and SI for 2 Years
CI - SI = P(R/100) 2
Very useful shortcut when compound interest and simple interest difference is asked for 2 years.
10. Difference Between CI and SI for 3 Years
CI - SI = P(R/100) 2(3 + R/100)
Important shortcut for 3-year problems where difference between compound and simple interest is asked.
How Compound Interest Works
Year 1
Interest is calculated on the original principal.
Year 2
Interest is calculated on principal + first year interest.
Next Years
Interest keeps getting added, so the growth becomes faster than simple interest.
Important Tricks for Compound Interest
Trick 1
For annual compound interest, always remember: A = P(1 + R/100) T
Trick 2
Half-yearly compounding means: Rate becomes half and time becomes double.
Trick 3
Quarterly compounding means: Rate becomes one-fourth and time becomes four times.
Trick 4
Population growth, machine growth, and investment growth all use the same CI pattern.
Trick 5
Depreciation problems use minus sign: Value = P(1 - R/100) T
Example Questions
Question 1
Find the compound interest on ₹1000 at 10% per annum for 2 years.
A = 1000(1 + 10/100) 2
A = 1000(1.1) 2
A = 1000 × 1.21 = ₹1210
CI = A - P = 1210 - 1000 = ₹210
Question 2
Find the amount on ₹5000 at 8% per annum compound interest for 3 years.
A = 5000(1 + 8/100) 3
A = 5000(1.08) 3
A = 5000 × 1.259712 = ₹6298.56
Amount = ₹6298.56
Question 3
A sum is compounded half-yearly at 12% per annum for 1 year. Find the amount if principal is ₹2000.
Half-yearly rate = 12/2 = 6%
Number of periods = 2 × 1 = 2
A = 2000(1 + 6/100) 2
A = 2000(1.06) 2
A = 2000 × 1.1236 = ₹2247.20
Question 4
Find the difference between Compound Interest and Simple Interest on ₹4000 for 2 years at 5% per annum.
CI - SI = P(R/100) 2
= 4000(5/100) 2
= 4000 × 25/10000
= ₹10
Question 5
The value of a machine decreases by 10% every year. Find its value after 2 years if initial value is ₹50,000.
Final Value = 50000(1 - 10/100) 2
= 50000(0.9) 2
= 50000 × 0.81
= ₹40,500
हिंदी में – चक्रवृद्धि ब्याज
अब इसी टॉपिक को आसान हिंदी में समझते हैं।
Compound Interest (चक्रवृद्धि ब्याज) गणित के Quantitative Aptitude का बहुत महत्वपूर्ण अध्याय है। इस टॉपिक से SSC, Banking, Railway, CAT, MBA entrance exams और placement tests में अक्सर प्रश्न पूछे जाते हैं।
अगर छात्र Compound Interest के formulas, growth pattern और shortcuts अच्छे से समझ लें, तो वे exam में questions को काफी जल्दी और सही तरीके से solve कर सकते हैं।
Compound Interest क्या है?
Compound Interest वह ब्याज है जो केवल मूलधन पर ही नहीं, बल्कि पहले से जुड़े हुए ब्याज पर भी लगाया जाता है।
महत्वपूर्ण शब्द
- मूलधन (P): प्रारंभिक राशि।
- दर (R): ब्याज की वार्षिक दर।
- समय (T): कुल समय।
- राशि (A): ब्याज जोड़ने के बाद कुल राशि।
- चक्रवृद्धि ब्याज (CI): compound interest से प्राप्त ब्याज।
महत्वपूर्ण सूत्र
A = P(1 + R/100) T
CI = A - P
CI = P[(1 + R/100) T - 1]
A = P(1 + R/200) 2T
A = P(1 + R/400) 4T
A = P(1 + r1/100)(1 + r2/100)...
Final Value = P(1 + R/100) T
Final Value = P(1 - R/100) T
CI - SI = P(R/100) 2
CI - SI = P(R/100) 2(3 + R/100)
आसान समझ
उदाहरण
उदाहरण 1
₹1000 पर 10% वार्षिक दर से 2 वर्ष का CI = ₹210
उदाहरण 2
₹5000 पर 8% वार्षिक दर से 3 वर्ष बाद राशि = ₹6298.56
उदाहरण 3
₹2000 पर 12% half-yearly compound interest के लिए 1 वर्ष बाद राशि = ₹2247.20
उदाहरण 4
₹4000 पर 5% की दर से 2 वर्ष में CI और SI का अंतर = ₹10
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