Simple & Compound Interest

Section A · Futures First International — Market Trading Intern OA

📌 What Has Been Asked (OA & Rounds)

Format	Typical Question Style
OA (MCQ)	"Find SI on ₹5000 at 8% for 3 years"
OA	"Difference between CI and SI for 2 years on ₹10,000 at 10% per annum"
OA	"A sum doubles in 5 years at SI. Find the rate of interest."
OA	"At what rate% will ₹8000 amount to ₹9261 in 3 years at CI compounded annually?"
Buzzer Round	"SI on 4000 at 5% for 2 years?" → instant answer
Interview	"If I invest ₹1 lakh at 12% compounded quarterly for 1 year, roughly what do I get?" — tests estimation

🧠 Core Concepts

1. Simple Interest (SI)

SI = (P × R × T) / 100

Amount = P + SI = P(1 + RT/100)

Where P = Principal, R = Rate% per annum, T = Time in years

2. Compound Interest (CI)

Amount = P × (1 + R/100)^T

CI = Amount − P = P[(1 + R/100)^T − 1]

Compounding frequency:

Annually: use R, T as is
Half-yearly: Rate = R/2, Time = 2T
Quarterly: Rate = R/4, Time = 4T

3. SI vs CI — The Key Difference (For 2 Years)

CI − SI = P × (R/100)²    [for 2 years only]

For 3 years:

CI − SI = P × (R/100)² × (3 + R/100)

4. Doubling Time

Method	Formula
SI	Time to double = 100/R years
CI (Rule of 72)	Time to double ≈ 72/R years

Example: At 8% SI → doubles in 100/8 = 12.5 years. At 8% CI → doubles in ≈72/8 = 9 years.

5. Population/Depreciation Problems

Population after n years = P × (1 + R/100)^n     [growth]
Value after n years = P × (1 − R/100)^n           [depreciation]

⚡ Speed Tricks for Futures First

Trick 1: SI is just "P × R × T / 100" — do it as fractions

SI on 5000 at 8% for 3 years = 5000 × 8 × 3 / 100 = ₹1200 (50 × 24 = 1200)

Trick 2: CI for 2 years using shortcut

Instead of (1 + R/100)²:

CI for 2 years = 2 × SI for 1 year + SI for 1 year × R/100

Or equivalently:

Amount = P + 2×(PR/100) + P(R/100)²

Example: P=10000, R=10%, T=2

SI for 1 year = 1000
CI = 2 × 1000 + 1000 × 10/100 = 2000 + 100 = ₹2100

Trick 3: "Sum doubles in n years at SI → rate = 100/n"

Triples → rate = 200/n
Quadruples → rate = 300/n

Trick 4: CI amounts form a GP

If you know amounts after year 1 and year 2:

Rate = [(A₂ − A₁) / A₁] × 100
Principal = A₁² / A₂

Trick 5: Quick (1 + R/100)^n values

R%	(1+R/100)²	(1+R/100)³
5%	1.1025	1.157625
10%	1.21	1.331
20%	1.44	1.728
25%	1.5625	1.953125

🎯 What Can Be Asked (Variations)

"The CI on a sum for 2 years at 10% is ₹2100. Find the sum." → CI for 2 years at 10% = P[(1.1)² − 1] = P × 0.21 → P = 2100/0.21 = ₹10,000
"A sum amounts to ₹6050 in 2 years at CI at 10%. Find the sum." → P × 1.21 = 6050 → P = ₹5000
"Difference between CI and SI for 2 years on a sum at 5% is ₹20. Find the sum." → P × (5/100)² = 20 → P × 0.0025 = 20 → P = ₹8000
"A certain sum triples in 8 years at SI. In how many years will it become 5 times?" → Triple means 200% interest in 8 years → rate = 25%. Five times = 400% → T = 400/25 = 16 years
"At what rate does ₹1000 become ₹1331 in 3 years at CI?" → (1 + R/100)³ = 1.331 = (1.1)³ → R = 10%

📝 Practice Questions (with Answers)

Q1. Find SI on ₹6400 at 7.5% for 2 years.

A: 6400 × 7.5 × 2 / 100 = 6400 × 15/100 = ₹960

Q2. What is the CI on ₹8000 at 10% for 2 years?

A: 8000 × 0.21 = ₹1680 (using shortcut: (1.1)² − 1 = 0.21)

Q3. The difference between CI and SI on a certain sum at 10% for 3 years is ₹620. Find the sum.

A: CI − SI for 3 years at 10% = P(0.1)²(3 + 0.1) = P × 0.031. So P × 0.031 = 620 → P = ₹20,000

Q4. A sum of money doubles in 6 years at SI. In how many years will it triple?

A: R = 100/6. To triple, need 200% → T = 200/(100/6) = 12 years

Q5. The CI on ₹4000 for 1 year at 10% compounded half-yearly is?

A: Rate = 5% per half, Time = 2 halves. A = 4000 × (1.05)² = 4000 × 1.1025 = ₹4410. CI = ₹410.

Q6. A machine worth ₹50,000 depreciates at 10% per year. Value after 2 years?

A: 50000 × (0.9)² = 50000 × 0.81 = ₹40,500

🔑 Exam Strategy

SI questions are pure speed — P×R×T/100 in fractions, done in 10 seconds
For CI, memorize (1.1)², (1.1)³, (1.05)², (1.2)² — covers most common rates
The "CI − SI for 2 years" shortcut P(R/100)² is asked almost every year — know it cold
For "amount doubles/triples at SI" → instant formula, don't derive
In trading context: CI is how compounding returns work — they may connect it to "compounding PnL" in interviews

04_simple_compound_interest.md