compound interest

💰 Compound Interest – Full Explanation

Compound interest is the interest earned in previous periods along with the principal amount Again the method of calculating interest. It is also known as Interest on Interest.

📌 Definition

By adding the interest earned at the end of each period to the principal amount, Calculation of interest for the next periodcompound interestis

🧮 Key formula

A = P (1 + R/100)^T

• ✔ A = Amount
• ✔ P = Principal
• ✔ R = Rate of Interest
• ✔ T = Time

💡 Compound Interest (CI)

CI = A - P

📊 Example

• ✔ P = ₹1000
• ✔ R = 10%
• ✔ T = 2 years

A = 1000 (1 + 10/100)²= 1000 × (1.1)²= 1000 × 1.21 = ₹1210

CI = 1210 - 1000 = ₹210

🔄 Separate Interest vs Compound Interest

• ✔ Separate interest → on principal only
• ✔ Compound interest → Interest on interest
• ✔ Compound interest will be higher

📏 Important notes

• ✔ Interest can be changed annually, semi-annually, quarterly
• ✔ Compound interest increases rapidly

Exams “What is Compound Interest formula?”, "What is the difference between CI and SI?" Questions like

🧮 Compound Interest Formulas

Key Formulas Used in Compound Interest Calculation Exams are very important. These help to calculate Amount and Interest.

📌 Key formula

A = P (1 + R/100)^T

• ✔ A = Amount
• ✔ P = Principal
• ✔ R = Rate of Interest
• ✔ T = Time (years)

💰 Compound Interest (CI)

CI = A - P

🔄 Alternative formulas

1️⃣ Principal (P)

P = A / (1 + R/100)^T

2️⃣ Rate (R)

R = \[ (A / P)^1/T- 1 \] × 100

3️⃣ Time (T)

T = log(A/P) / log(1 + R/100)

📊 Half-Yearly

• ✔ R → R/2
• ✔ T → 2T

A = P (1 + R/200)^2T

📊 Quarterly

• ✔ R → R/4
• ✔ T → 4T

A = P (1 + R/400)^4T

📘 Shortcut (2 years)

CI = P(R/100)²

📏 Important notes

• ✔ Compound Interest = Interest on Interest
• ✔ Time unit must match interest period
• ✔ More compounding → more interest

“Compound Interest formula” in exams. “How to calculate half yearly interest?” Questions like

🧮 Compound Interest – 10 examples

📘 Example 1

P = 1000, R = 10%, T = 2

A = 1000(1.1)²= 1210 → CI = ₹210

📘 Example 2

P = 2000, R = 5%, T = 2

A = 2000(1.05)²= 2205 → CI = ₹205

📘 Example 3

P = 1500, R = 8%, T = 3

A = 1500(1.08)³= 1889.57 → CI ≈ ₹389.57

📘 Example 4

P = 5000, R = 6%, T = 2

A = 5000(1.06)²= 5618 → CI = ₹618

📘 Example 5

P = 2500, R = 4%, T = 3

A = 2500(1.04)³= 2812 → CI = ₹312

📘 Example 6

P = 3000, R = 7%, T = 2

A = 3000(1.07)²= 3434.7 → CI ≈ ₹434.7

📘 Example 7

P = 1200, R = 9%, T = 2

A = 1200(1.09)²= 1425.48 → CI ≈ ₹225.48

📘 Example 8

P = 4000, R = 5%, T = 3

A = 4000(1.05)³= 4630.5 → CI ≈ ₹630.5

📘 Example 9

P = 3500, R = 6%, T = 2

A = 3500(1.06)²= 3932.6 → CI ≈ ₹432.6

📘 Example 10

P = 10000, R = 3%, T = 2

A = 10000(1.03)²= 10609 → CI = ₹609

⚡ Compound Interest – Shortcut & Tricks

Some shortcut methods can be very helpful in making compound interest accounts faster. These will help you save time in competitive exams.

🚀 Trick 1: Shortcut for 2 years

CI = P(R/100)²

👉 Difference (CI – SI) = P (R/100)²

📘 Example

P = 1000, R = 10%

Difference = 1000 × (10/100)²= ₹10

🚀 Trick 2: Shortcut for 3 years

CI – SI = P (R/100)²(3 + R/100)

📘 Example

P = 1000, R = 10%

= 1000 × (0.1)²× (3.1) = ₹31

🚀 Trick 3: Small % (Approximation)

• ✔ (1 + x)²≈ 1 + 2x
• ✔ (1 + x)³≈ 1 + 3x

👉 Fast calculation at small interest rates

🚀 Trick 4: Doubling Trick

Amount doubles when:

Time ≈ 72 / Rate

📘 Example

R = 8%

Time ≈ 72 / 8 = 9 years

🚀 Trick 5: Half-Yearly Shortcut

• ✔ R → R/2
• ✔ T → 2T

👉 Faster calculation using modified values

🚀 Trick 6: Percentage Method

10% → ×1.1 5% → ×1.05 20% → ×1.2

📘 Example

1000 at 10% for 2 years

1000 × 1.1 × 1.1 = ₹1210

🚀 Trick 7: SI vs CI Difference

• ✔ 2 years → P(R/100)²
• ✔ 3 years → P(R/100)²(3 + R/100)

📏 Important notes

• ✔ More compounding → more interest
• ✔ Shortcut mostly for exams
• ✔ Practice is important

“CI vs SI difference” in competitive exams. Questions like “Shortcut method solve” come up a lot.