SarwaSamadhan

Difference between compound and simple interest for 2 years: P × (r/100)²

2 वर्ष के चक्रवृद्धि और साधारण ब्याज का अंतर: P × (r/100)²

For 2 years, compound interest is more than simple interest by exactly P × (r/100)² — the interest earned on the first year's interest. No need to calculate both.

2 वर्ष के लिए चक्रवृद्धि ब्याज, साधारण ब्याज से ठीक P × (r/100)² अधिक होता है — यानी पहले साल के ब्याज पर मिला ब्याज। दोनों अलग-अलग निकालने की ज़रूरत नहीं।

The shortcut

CI − SI (2 years) = P × (r/100)². In the second year, compound interest also earns interest on the first year's interest; that extra is the whole difference.

  1. Write r/100 as a decimal.
  2. Square it.
  3. Multiply by the principal P.
Example P = ₹10,000, r = 10%, 2 years.
10,000 × (0.1)² = 10,000 × 0.01 = ₹100
Example P = ₹5,000, r = 8%, 2 years.
5,000 × 0.0064 = ₹32

Working backwards

Exams often give the difference and ask for P. Divide the difference by (r/100)².

Example Difference = ₹20 at 5% for 2 years. Principal?
20 ÷ (0.05)² = 20 ÷ 0.0025 = ₹8,000

Try it yourself · अभ्यास

  1. P = ₹8,000, r = 5%, 2 years. CI − SI?
    Show answer

    8,000 × 0.0025 = ₹20

  2. Difference ₹100 at 10% for 2 years. P?
    Show answer

    100 ÷ 0.01 = ₹10,000