🏦 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.
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).
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.
• 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.
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
AnimationAfter 10 years: SI gives a steady ₹20k. CI snowballs to ₹25,937. The longer you wait, the more dramatic the gap.
Interest Calculator
CalculatorP = ₹ · R = % · T = yr
CI − SI = ₹310 (because of compounding)
P=₹ · R=% · T= yr · Compounded:
Amount = ₹12,100 · Interest = ₹2,100