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.2 वर्ष के लिए 20% वार्षिक चक्रवृद्धि ब्याज पर उधार दी गई एक धनराशि पर, यदि ब्याज अर्धवार्षिक देय हो तो वार्षिक देय होने की तुलना में ₹482 अधिक प्राप्त होता है। उधार दी गई धनराशि ज्ञात कीजिए।

1. A₹15,000
2. B₹13,000
3. C₹18,000
4. D₹20,000

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Correct answer: D. ₹20,000

Explanation

Annually: amount = P(1 + 20/100)² = 1.44P. Half-yearly: rate = 10% per half-year for 4 periods, amount = P(1.1)⁴ = 1.4641P. Difference = 1.4641P − 1.44P = 0.0241P = 482, so P = 482 ÷ 0.0241 = ₹20,000.वार्षिक: मिश्रधन = P(1 + 20/100)² = 1.44P। अर्धवार्षिक: दर = प्रति छमाही 10%, 4 अवधियाँ, मिश्रधन = P(1.1)⁴ = 1.4641P। अंतर = 1.4641P − 1.44P = 0.0241P = 482, अतः P = 482 ÷ 0.0241 = ₹20,000।