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A person borrowed Rs. 1024 for two years at 50% interest per annum but payable half-yearly. If the interest was compound interest, then how much amount would he have to pay back at the end of the loan period?

(1) Rs. 2048
(2) Rs. 2500
(3) Rs. 5344
(4) Rs. 5184

किसी व्यक्ति ने 50% प्रति वर्ष ब्याज़ दर पर परन्तु अर्ध-वार्षिक रूप से देय, 1024 रुपये दो वर्षों के लिए उधार लिये, यदि ब्याज़, चक्रवृद्धि ब्याज़ था तो ऋण अवधि की समाप्ति पर उसे कितनी राशि का वापसी भुगतान करना होगा?

(1) 2048 रुपये
(2) 2500 रुपये
(3) 5344 रुपये
(4) 5184 रुपये
This Question came in
UGC-NET-Hindi-08-January-2025-Shift-1-Q19
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Detailed Explanation & Answer
Principal = Rs. 1024
Rate = 50% per annum, compounded half-yearly
So, half-yearly rate = 25%
Time = 2 years = 4 half-years

Formula for compound interest:
Amount = P × (1 + r/100)ⁿ
= 1024 × (1 + 25/100)⁴
= 1024 × (1.25)⁴
= 1024 × 2.4414
= Rs. 2500

So, the person would have to pay back Rs. 2500 at the end of 2 years.
मूलधन = 1024 रुपये
दर = 50% प्रति वर्ष, अर्धवार्षिक चक्रवृद्धि ब्याज
अतः, अर्धवार्षिक दर = 25%
समय = 2 वर्ष = 4 अर्ध-वर्ष

चक्रवृद्धि ब्याज का सूत्र:
राशि = P × (1 + r/100)ⁿ
= 1024 × (1 + 25/100)⁴
= 1024 × (1.25)⁴
= 1024 × 2.4414
= 2500 रुपये

अतः, व्यक्ति को 2 वर्ष के अंत में 2500 रुपये वापस करने होंगे।
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