What is the difference between the compound interests on Rs.23000 for 1 year at 10% per annum compounded yearly and half-yearly? (In Rs.)

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UP Police SI (दरोगा) Official PYP (Held On: 16 Nov 2021 Shift 2)
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  1. 55.5
  2. 53.5
  3. 57.5
  4. 51.5

Answer (Detailed Solution Below)

Option 3 : 57.5
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UP Police SI (दरोगा) Official PYP (Held On: 2 Dec 2021 Shift 1)
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Detailed Solution

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Given:

Principal (P) = ₹23,000

Rate (R) = 10% per annum

Time (T) = 1 year

Formula Used:

Compound Interest (CI) = A - P

Amount (A) = P × (1 + R/100)t (for yearly)

Amount (A) = P × (1 + R/2 ÷ 100)2t (for half-yearly)

Calculation:

Yearly Compounding:

A1 = 23000 × (1 + 10/100)1 = 23000 × 1.10 = ₹25,300

CI1 = 25,300 - 23,000 = ₹2,300

Half-Yearly Compounding:

A2 = 23000 × (1 + 5/100)2 = 23000 × (1.05)2 = 23000 × 1.1025 = ₹25,357.50

CI2 = 25,357.50 - 23,000 = ₹2,357.50

Difference:

CI2 - CI1 = 2357.50 - 2300 = ₹57.50

∴ The difference is ₹57.50.

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