Useful for RBI, CSAT, BANKING ETC

📍 Overview

• Relevance: 1–3 questions in RBI Grade B Phase 1 (worth 2–6 marks).
• Skills Tested: Formula accuracy, speed, logical reasoning, and approximation.
• Integrated With: Profit/Loss, Time Value of Money, Data Interpretation.

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1️⃣ Introduction to SI & CI

Concept	Description
Simple Interest (SI)	Interest on principal only. Formula: SI = (P × R × T) / 100
Compound Interest (CI)	Interest on principal + past interest. Formula: CI = A - P, where A = P(1 + R/100)^T
Key Difference	SI grows linearly; CI grows exponentially
Application Areas	Loans, savings, fixed deposits, installment schemes
Compounding Types	Annual (default), Half-Yearly, Quarterly

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2️⃣ Core Formulas & Variants

Formula	Use	Example
SI = (P × R × T)/100	Basic SI	₹10,000 @ 5% for 3 yrs = ₹1,500
A (SI) = P[1 + (RT)/100]	Total amount in SI	₹11,500
A (CI) = P(1 + R/100)^T	Amount in CI	₹11,576.25
CI = A – P	Interest from CI	₹1,576.25
CI (Half-Yearly)	A = P[1 + (R/2)/100]^(2T)	₹11,025 (for 1 yr @ 10%)
CI (Quarterly)	A = P[1 + (R/4)/100]^(4T)	As per quarter calc
Difference (CI – SI, 2 yrs)	P(R/100)^2 × (300+R)/300	Useful for small R
Effective Rate	[(1 + R/100)^T - 1] × 100/T	≈10.25% for 2 yrs at 10%
EMI (CI)	P × R(1 + R)^T / [(1 + R)^T – 1]	For compound interest loans
Reverse R (CI)	R = [(A/P)^(1/T) – 1] × 100	Find rate if A and P known
Rule of 72	Doubling time: T ≈ 72/R	9 yrs @ 8%

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3️⃣ Speed Tricks & Shortcuts

Trick	How It Helps	Example
Quick SI Estimation	Use 10% = P/10 rule	₹5,000 @ 8% for 4 yrs = ₹1,600
CI ≈ SI + Adjustment	Approx. for small T	SI + (SI × R)/(200)
CI – SI (Shortcut)	P(R^2)/10,000 (for 2 yrs)	₹100 for ₹10,000 @ 10%
Successive Rates	R1 + R2 + (R1×R2)/100	For year-on-year increases
Reverse Principal	P = A / (1 + R/100)^T	For CI
Installment Trick (SI)	Convert to linear series	Requires equation setup
Rule of 114	Time to triple = 114/R	Triple @ 12% = 9.5 yrs
Fractional Periods	Convert time to months or use decimals	1.5 yrs = 3 half-years

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4️⃣ Step-by-Step Solved Examples

Example 1: Simple Interest

Q: ₹8,000 @ 7% for 5 yrs → SI = ?
A: SI = (8000 × 7 × 5)/100 = ₹2,800

Example 2: Compound Interest

Q: ₹5,000 @ 10% CI for 3 yrs → Amount = ?
A: A = 5000 × (1.1)^3 = ₹6,655 → CI = ₹1,655

Example 3: Difference Between CI & SI

Q: CI – SI = ₹197.12 @ 8%, 3 yrs. Find P.
A: P = 197.12 / 0.019712 = ₹10,000

Example 4: CI Half-Yearly

Q: ₹10,000 @ 12%, 1.5 yrs, half-yearly → CI = ?
A: A = 10000 × (1.06)^3 = ₹11,910.16 → CI ≈ ₹1,910

Example 5: Mixed Rate SI

Q: ₹36,000 split between 12% & 10% SI. Total after 2 yrs = ₹43,920. How much at 12%?
A: ₹18,000 at 12%

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5️⃣ Practice Set (with Solutions)

#	Question	Short Solution
1	₹12,000 @ 5% for 4 yrs	SI = ₹2,400
2	A = ₹7,200, R = 20%, T = 2 yrs	P = ₹5,000
3	SI = ₹900, T = 3 yrs, R = 10%	P = ₹3,000
4	₹4,000 @ 15%, CI, quarterly, 2 yrs	A ≈ ₹5,352
5	Arun vs Bhavesh SI rate comparison	x = 7%
6	Diff (CI – SI) = ₹197.12 @ 8%, 3 yrs	P = ₹10,000
7	₹50,000 loan @ 10% CI, 2 equal installments	X ≈ ₹27,231
8	₹1,000 → ₹1,331 @ 10%	T = 3 yrs
9	SI > CI by ₹600, same P	Solve with equations
10	Effective CI for 12%, half-yearly	≈ 12.36%

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6️⃣ RBI Previous Year Questions (PYQs)

Year	Pattern/Question	Solution Summary
2022	Mix SI @ 12% & 10% → Total ₹43,920	₹18,000 @ 12%
2021	A: x% for 6 yrs; B: (x–2)% for 7 yrs → A = 1.2B	x = 7%
2023	CI – SI diff = ₹197.12 @ 8%	P = ₹10,000
2024	CI triples in 5 yrs → When will it 9x?	10 years
2020	CI – SI on ₹5,000 @ 10%, 3 yrs	₹155

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7️⃣ Exam Smart Strategy

Tip	Description
Time Mgmt	Use elimination & approximations
Common Errors	Forgetting compounding frequency or wrong formula
Practice Plan	30 mins daily; 20–30 Qs + mock test
Resources	cracktarget.com
Exam Day	Watch for interest in DI; plug in P values smartly