​A sum of money lent at compound interest for 2 years at 20% per annum would fetch ₹482 more if the interest was payable half-yearly than if it was payable annually. Find the sum of money lent.​

Correct option is D

Given:
Difference in amount = ₹482
Rate = 20% per annum
Time = 2 years
​
Formula:
Amount when compounded annually =
​$$A_1 = P \times \left(1 + \frac{R}{100}\right)^2 \\$$​​
Amount when compounded half-yearly =
​$$A_2 = P \times \left(1 + \frac{\frac{R}{2}}{100}\right)^4 \\$$​​

Given difference:
A₂ − A₁ = ₹482

Solution:
Step 1: Express both amounts:

A₁ = P × (1.2)² = P × 1.44

A₂ = P × (1.1)⁴ = P × 1.4641

Step 2: Set up the difference equation:

A₂ − A₁ = P × (1.4641 − 1.44) = ₹482

P × 0.0241 = ₹482

Step 3: Calculate P:

P = 482 ÷ 0.0241

P = ₹20,000

Final Answer: (d) ₹20,000