Question 26 of 45intermediate🔧 ApplyNumerical4 marks

Bank of Yahapur offers an interest of 10% p.a. Compare how much one gets if they deposit ₹20,000 for a period of 2 years with compounding and without compounding annually.

Correct Answer

Without Compounding: Formula: Interest = P × r × t Interest = 20,000×0.10000 \times 0.10 × 2 = ₹4,000 Total = 20,000 + 4,000 = ₹24,000

With Compounding: Formula: Amount = P × (1 + r)^t Year 1: 20,000×1.10000 \times 1.10 = ₹22,000 Year 2: 22,000×1.10000 \times 1.10 = ₹24,200

Difference: Difference = 24,200 - 24,000 = ₹200 ∴ One gets ₹200 more with compounding.

Exercise: Figure it Out (Section 4) | Q: 1 | (Page Page 22)
For More Understanding

Explanation

The chapter explains both simple interest (without compounding) and compound interest. Without compounding: Interest = P × r × t = 20,000×0.10000 \times 0.10 × 2 = ₹4,000. With compounding: Amount = P × (1 + r)^t = 20,000 × (1.10)² = ₹24,200.

Solution Steps

  1. Without compounding:

  2. Interest = 20,000×0.10000 \times 0.10 × 2 = ₹4,000

  3. Total = 20,000 + 4,000 = ₹24,000

  4. With compounding:

  5. Year 1: 20,000×1.10000 \times 1.10 = ₹22,000

  6. Year 2: 22,000×1.10000 \times 1.10 = ₹24,200

  7. Difference: ₹24,200 - ₹24,000 = ₹200

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