Math · Aptitude · Chapter 06

🏦 Simple & Compound Interest

SI vs CI — formulas and the power of compounding.

💡 Interest: SI vs CI

Simple Interest (SI) — interest calculated only on the original principal each year. Doesn't grow.

Compound Interest (CI) — interest gets added to principal, and next year's interest is calculated on the new bigger amount. Grows exponentially.

Simple Interest
SI = (P × R × T) / 100
Amount (SI)
A = P + SI = P(1 + RT/100)
Compound Amount
A = P(1 + R/100)ᵀ
Compound Interest
CI = A − P

P = Principal · R = Rate (per annum %) · T = Time (in years)

Example: ₹10,000 at 10% for 3 years.
SI = (10000 × 10 × 3)/100 = ₹3,000 → Amount = ₹13,000
CI = 10000 × (1.10)³ − 10000 = 13,310 − 10,000 = ₹3,310
CI is always more than SI (for T > 1 year).

⚡ CI − SI for 2 years

For 2 years at rate R%: CI − SI = P × (R/100)²

Example: P = ₹5000, R = 10%, T = 2 → CI − SI = 5000 × 0.01 = ₹50. No need for full calc.

⚡ Compounding more than yearly

• Half-yearly: A = P(1 + R/200)²ᵀ
• Quarterly: A = P(1 + R/400)⁴ᵀ
• Monthly: A = P(1 + R/1200)¹²ᵀ

More frequent compounding → slightly more interest.

⚡ Rule of 72 (doubling time)

To find years for money to double at rate R% (compound): T ≈ 72 / R.

At 9%, money doubles in 72/9 = 8 years. At 12%, in 6 years. Quick mental check.

🎬

SI vs CI Growth Over Time

Animation
₹10,000 AT 10% — SI (LINE) VS CI (CURVE) Years Amount (₹) 0 2 4 6 8 10 10k 15k 20k 25k 30k SI CI ₹20,000 ₹25,937

After 10 years: SI gives a steady ₹20k. CI snowballs to ₹25,937. The longer you wait, the more dramatic the gap.

🧮

Interest Calculator

Calculator
🧮 Principal · Rate · Time

P = ₹ · R = % · T = yr

SI
₹3,000
CI
₹3,310
Amount (SI)
₹13,000
Amount (CI)
₹13,310

CI − SI = ₹310 (because of compounding)

📅 Compound frequency

P=₹ · R=% · T= yr · Compounded:

Amount = ₹12,100 · Interest = ₹2,100

Practice (SSC): The difference between CI and SI on ₹5000 for 2 years at 8% per annum is?
Shortcut for 2 years: CI − SI = P × (R/100)² = 5000 × (8/100)² = 5000 × 0.0064 = ₹32.
Practice (Banking): A sum doubles in 8 years at simple interest. In how many years will it triple?
If it doubles in 8 years, SI = P. So PR×8/100 = P → R = 12.5%. To triple, SI = 2P. So PR×T/100 = 2P → T = 200/R = 200/12.5 = 16 years.
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