Compound Interest

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💰 Compound Interest - The Basics

Method of calculating interest on both principal and interest!

📚 What is compound interest?

Compound Interestis interest calculated on both principal and accrued interest.

🎯 Important Note:
called "interest on interest".
Interest accrues every period.

⭐ Key Terms

artifice	English	Code	Explanation
Original	Principal	P	Initial investment amount
Interest rate	Rate of Interest	R	Annual interest percentage
Period	Time	n	How many years/periods?
compound interest	Compound Interest	CI	Total interest earned
sum	Amount	A	Principal + Compound Interest

📐 Basic formula

A = P(1 + R/100)ⁿ

Amount = Principal × (1 + Rate/100)^Term

CI = A - P

Compound Interest = Amount - Principal

🔄 Interest Calculation Periods

Type	Period	value of n	R value
Annually	Once a year	n = years	R = R%
Half-yearly	Once in 6 months	n = 2 × years	R = R/2 %
Quarterly	Once in 3 months	n = 4 × years	R = R/4 %
Monthly	Once a month	n = 12 × years	R = R/12 %

📊 Simple understanding - example

Question:What is the amount of ₹1000 invested for 2 years at 10% compound interest?

Solution:

P = ₹1000, R = 10%, n = 2
A = P(1 + R/100)ⁿ
A = 1000(1 + 10/100)²
A = 1000 × (1.1)²
A = 1000 × 1.21 =₹1210

CI:1210 - 1000 =₹210

SI (Comparison):1000 × 10 × 2 / 100 = ₹200

CI - SI = ₹10 more!

📈📉 Separate interest vs compound interest

feature	Separate Interest (SI)	Compound Interest (CI)
Calculation of interest	On the original only	On principal + previous interest
Every year	Interest is equal	Interest will increase
For 1 year	SI = CI	SI = CI (equal to)
More than 1 year	SI < CI	CI > SI

🎯 Important Notes

SI = CI (equal) for 1 year
CI - SI = SI × R / 100 for 2 years
Half yearly interest > Annual interest
Quarterly interest > Half yearly interest
Compound interest is always higher than individual interest (over 1 year).

📐 Compound Interest - Key Formulas

All Formulas Essential for TNPSC Exam!

🔢 Basic formulas

to find out	formula
Amount (A)	A = P(1 + R/100)ⁿ
Compound Interest (CI)	CI = A - P = P[(1 + R/100)ⁿ - 1]
Original (P)	P = A / (1 + R/100)ⁿ

📊 Half Yearly / Quarterly Formulas

Type	formula
Half-yearly	A = P(1 + R/200)²ⁿ
Quarterly	A = P(1 + R/400)⁴ⁿ
Monthly	A = P(1 + R/1200)¹²ⁿ

💰 CI - SI Difference Formulas

Period	CI - SI formula
2 years	CI - SI = P × (R/100)² = SI × R / 100
3 years	CI - SI = P × (R/100)² × (3 + R/100)

Period

CI - SI formula

2 years

CI - SI = P × (R/100)²

= SI × R / 100

3 years

CI - SI = P × (R/100)² × (3 + R/100)

💡 2 Year Shortcut:CI - SI = 1 year SI on SI

📈 Different ratios formula

If first year is R₁%, second year is R₂%, third year is R₃%:

A = P × (1 + R₁/100) × (1 + R₂/100) × (1 + R₃/100)

📉 Depreciation formulas

condition	formula
Depreciation	V = P(1 - R/100)ⁿ
Depopulation	P = P₀(1 - R/100)ⁿ

👥 Population / Growth Formulas

condition	formula
Population increase	P = P₀(1 + R/100)ⁿ
Price rise	New Price = Old Price × (1 + R/100)ⁿ

🔄 Double / Triple formulas

condition	formula
(Rule of 72)	n ≈ 72 / R
be n times	(1 + R/100)ⁿ = times

📋 Formula summary

To find A:P(1+R/100)ⁿ
To find CI:A-P
Half Yearly:R/2, n×2

Quarterly:R/4, n×4
2 Year CI-SI:P(R/100)²
Double:72/R years

📝 Compound Interest - 10 Key Examples

Frequently Asked Question Types in TNPSC Exam!

📌 Example 1: Basic CI calculation

Question:What is the amount if ₹8000 is invested for 2 years at 10% compound interest?

Solution:
P = ₹8000, R = 10%, n = 2

A = P(1 + R/100)ⁿ
A = 8000(1 + 10/100)²
A = 8000 × (1.1)²
A = 8000 × 1.21 = ₹9680

Answer: ₹9680

📌 Example 2: Finding CI

Question:If ₹5000 is invested at 8% compound interest for 3 years what is the compound interest?

Solution:
P = ₹5000, R = 8%, n = 3

A = 5000(1 + 8/100)³
A = 5000 × (1.08)³
A = 5000 × 1.259712 = ₹6298.56

CI = A - P = 6298.56 - 5000 = ₹1298.56

Answer: ₹1298.56

📌 Example 3: Half yearly interest

Question:If ₹10000 is invested for 1 year at 10% compounded semi-annually, the amount will be?

Solution:
P = ₹10000, R = 10%, n = 1 year
Semiannually: R = 10/2 = 5%, n = 1×2 = 2

A = 10000(1 + 5/100)²
A = 10000 × (1.05)²
A = 10000 × 1.1025 = ₹11025

Answer: ₹11025

📌 Example 4: Quarterly interest

Question:CI if ₹16000 is invested for 9 months at 20% compounded quarterly?

Solution:
P = ₹16000, R = 20%, n = 9 months = 3/4 year
Quarter: R = 20/4 = 5%, n = 3 (quarters)

A = 16000(1 + 5/100)³
A = 16000 × (1.05)³
A = 16000 × 1.157625 = ₹18522

CI = 18522 - 16000 = ₹2522

Answer: ₹2522

📌 Example 5: CI - SI Difference

Question:What is the difference of CI and SI for ₹5000 at 10% interest for 2 years?

Solution:
P = ₹5000, R = 10%, n = 2

Method 1:
CI - SI = P × (R/100)²
CI - SI = 5000 × (10/100)²
CI - SI = 5000 × 0.01 = ₹50

Method 2:
SI = 5000 × 10 × 2 / 100 = ₹1000
CI - SI = SI × R/100 = 1000 × 10/100 = ₹50

Answer: ₹50

📌 Example 6: Original invention

Question:A sum becomes ₹12100 in 2 years at 10% CI. What is original?

Solution:
A = ₹12100, R = 10%, n = 2

P = A / (1 + R/100)ⁿ
P = 12100 / (1 + 10/100)²
P = 12100 / (1.1)²
P = 12100 / 1.21 = ₹10000

Answer: ₹10000

📌 Example 7: Different proportions

Question:₹10000 at 10% in first year, 20% in second year Amount in CI?

Solution:
P = ₹10000, R₁ = 10%, R₂ = 20%

A = P × (1 + R₁/100) × (1 + R₂/100)
A = 10000 × (1 + 10/100) × (1 + 20/100)
A = 10000 × 1.1 × 1.2
A = 10000 × 1.32 = ₹13200

Answer: ₹13200

📌 Example 8: Doubling period

Question:How many years will it take for a sum to double at 12% compound interest?

Solution:
R = 12%

To use Rule of 72:
n ≈ 72 / R
n ≈ 72 / 12 = 6 years

Answer: About 6 years

📌 Example 9: Population Growth

Question:A city has a population of 50000. Annual growth is 4%. Population after 2 years?

Solution:
P₀ = 50000, R = 4%, n = 2

P = P₀(1 + R/100)ⁿ
P = 50000(1 + 4/100)²
P = 50000 × (1.04)²
P = 50000 × 1.0816 = 54080

Answer: 54080 people

Example 10: Depreciation

Question:A car costs ₹500000. Annual depreciation is 10%. Value after 3 years?

Solution:
P = ₹500000, R = 10%, n = 3

V = P(1 - R/100)ⁿ
V = 500000(1 - 10/100)³
V = 500000 × (0.9)³
V = 500000 × 0.729 = ₹364500

Answer: ₹3,64,500

📊 Important notes

Note that (1.1)² = 1.21, (1.1)³ = 1.331
Semiannual = R/2, n×2; Quarter = R/4, n×4
CI - SI (2 year) = P(R/100)² is very important
Growth: (1 + R/100), Depreciation: (1 - R/100)

⚡ Compound Interest - Crossroads

Super Tricks to Save Time in TNPSC Exam!

🚀 Trick 1: 2 Year CI Fast Track

2-year CI = 2 × SI + (SI × R / 100)

Or

CI = SI + SI²/(100×P)

Example:₹10000, 10%, 2 yr

SI = 10000 × 10 × 2 / 100 = ₹2000

CI = 2000 + (2000 × 10/100) = 2000 + 200 =₹2200

🚀 Trick 2: CI - SI (2 years) Super Shortcut

CI - SI = P × (R/100)²

Or

CI - SI = SI × R / (2 × 100)× 2
CI - SI = SI over 1 year SI

Example:₹5000, 10%, 2 yr

CI - SI = 5000 × (10/100)² = 5000 × 0.01 =₹50

🚀 Trick 3: Rule of 72 (Double)

Doubling period ≈ 72 / R

Interest rate	Double period
6%	72/6 = 12 years
8%	72/8 = 9 years
9%	72/9 = 8 years
12%	72/12 = 6 years

🚀 Trick 4: Key (1+R/100)ⁿ values

R%	n=2	n = 3
5%	1.1025	1.157625
10%	1.21	1.331
20%	1.44	1.728
25%	1.5625	1.953125

💡 Memory:10% → 1.1, 1.21, 1.331 (1.1 × 1.1 × 1.1)

🚀 Trick 5: Effective Rate of Interest

Effective Rate of Half Yearly Interest:
E = (1 + R/200)² - 1 = R + R²/400

Example:10% Effective Rate of Half Yearly Interest

E = 10 + 100/400 = 10 + 0.25 =10.25%

🚀 Trick 6: CI from SI Shortcut

For 2 years:CI = SI × (1 + R/200)
For 3 years:CI = SI × (1 + R/100 + R²/30000)

Example:SI = ₹2000, R = 10%, 2 yr

CI = 2000 × (1 + 10/200) = 2000 × 1.05 =₹2100

🚀 Trick 7: Calculating CI by year

Interest on previous amount every year:

1st year CI = P × R/100
2nd year CI = (P + 1st CI) × R/100
3rd year CI = (P + 1st CI + 2nd CI) × R/100

Example:₹10000, 10%

1st year = 10000 × 10/100 = ₹1000

2nd year = 11000 × 10/100 = ₹1100

Total CI = 1000 + 1100 =₹2100

🚀 Trick 8: In the CI-SI difference to find the original

If CI - SI = D for 2 years:

P = D × (100/R)²

Example:CI - SI = ₹40, R = 10%

P = 40 × (100/10)² = 40 × 100 =₹4000

🚀 Trick 9: Continuous CI values

Increase in CI each year = previous CI × R/100

Example:at 10% interest

If 1st year CI = ₹1000

2nd year CI = 1000 + (1000 × 10/100) =₹1100

3rd year CI = 1100 + (1100 × 10/100) =₹1210

🚀 Trick 10: Find the ratio

If A₁ (1 year amount), A₂ (2 year amount) is known:

R = [(A₂ - A₁) / A₁] × 100

Example:A₁ = ₹11000, A₂ = ₹12100

R = [(12100 - 11000) / 11000] × 100

R = (1100/11000) × 100 =10%

📊 TNPSC Frequently Asked Categories

Question type	Crossroads
Calculate CI	A = P(1+R/100)ⁿ, CI = A-P
CI - SI (2 Year)	P × (R/100)²
half year	R/2, n×2
Double period	72/R
Population	P(1+R/100)ⁿ
Depreciation	P(1-R/100)ⁿ

💡 Important memory tips

A = P(1+R/100)ⁿ- Basic formula
CI = A - P- Always remember
CI - SI = P(R/100)²- For 2 years
72/R- Years to double
Growth: +R, Depreciation: -R
Semiannual: R/2, n×2
Quarter: R/4, n×4

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Learning Content

💰 Compound Interest - The Basics

📚 What is compound interest?

⭐ Key Terms

📐 Basic formula

A = P(1 + R/100)ⁿ

CI = A - P

🔄 Interest Calculation Periods

📊 Simple understanding - example

📈📉 Separate interest vs compound interest

🎯 Important Notes

📐 Compound Interest - Key Formulas

🔢 Basic formulas

A = P(1 + R/100)ⁿ

CI = A - P = P[(1 + R/100)ⁿ - 1]

P = A / (1 + R/100)ⁿ

📊 Half Yearly / Quarterly Formulas

A = P(1 + R/200)²ⁿ

A = P(1 + R/400)⁴ⁿ

A = P(1 + R/1200)¹²ⁿ

💰 CI - SI Difference Formulas

CI - SI = P × (R/100)²

CI - SI = P × (R/100)² × (3 + R/100)

📈 Different ratios formula

A = P × (1 + R₁/100) × (1 + R₂/100) × (1 + R₃/100)

📉 Depreciation formulas

V = P(1 - R/100)ⁿ

P = P₀(1 - R/100)ⁿ

👥 Population / Growth Formulas

P = P₀(1 + R/100)ⁿ

New Price = Old Price × (1 + R/100)ⁿ

🔄 Double / Triple formulas

n ≈ 72 / R

(1 + R/100)ⁿ = times

📋 Formula summary

📝 Compound Interest - 10 Key Examples

📌 Example 1: Basic CI calculation

📌 Example 2: Finding CI

📌 Example 3: Half yearly interest

📌 Example 4: Quarterly interest

📌 Example 5: CI - SI Difference

📌 Example 6: Original invention

📌 Example 7: Different proportions

📌 Example 8: Doubling period

📌 Example 9: Population Growth

Example 10: Depreciation

📊 Important notes

⚡ Compound Interest - Crossroads

🚀 Trick 1: 2 Year CI Fast Track

🚀 Trick 2: CI - SI (2 years) Super Shortcut

🚀 Trick 3: Rule of 72 (Double)

🚀 Trick 4: Key (1+R/100)ⁿ values

🚀 Trick 5: Effective Rate of Interest

🚀 Trick 6: CI from SI Shortcut

🚀 Trick 7: Calculating CI by year

🚀 Trick 8: In the CI-SI difference to find the original

🚀 Trick 9: Continuous CI values

🚀 Trick 10: Find the ratio

📊 TNPSC Frequently Asked Categories

💡 Important memory tips

General Studies

General Science

Current events

Geography

History and Culture of India

Constitution of India

Indian Economy

Indian National Movement

History, Culture, Tradition and Socio-Political Movements of Tamil Nadu

Development Administration in Tamil Nadu

Competence and mental intelligence