Question:
A sum of Rs. 5,000 amounts to Rs. 6,050 in 4 years at a certain rate of interest, compounded annually. Find the amount received after 2 years when Rs. 1,800 are invested at the same rate of compound interest (compounded annually).
5,000 रुपये की राशि एक निश्चित चक्रवृद्धि ब्याज दर पर 4 वर्षों में 6,050 रुपये हो जाती है। जब समान चक्रवृद्धि ब्याज दर पर 1,800 रुपये 2 वर्षों के लिए निवेश किए जाते हैं, तो प्राप्त राशि ज्ञात कीजिए।
Options:
- Rs. 1,980
- Rs. 2,058
- Rs. 2,145
- Rs. 2,200
- Rs. 1,980
- Rs. 2,058
- Rs. 2,145
- Rs. 2,200
Correct Answer: a)
Explanation:
We have \((1 + r)^4 = \dfrac{6050}{5000} = \dfrac{121}{100}\).
Taking the square root:
\((1 + r)^2 = \sqrt{\dfrac{121}{100}} = \dfrac{11}{10} = 1.1\).
Amount after 2 years on Rs. 1,800:
\(A = 1800 \times (1 + r)^2 = 1800 \times 1.1 = \text{Rs. } 1,980\).
\((1 + r)^4 = \dfrac{6050}{5000} = \dfrac{121}{100}\)।
वर्गमूल लेने पर: \((1 + r)^2 = \dfrac{11}{10} = 1.1\)।
1,800 रुपये पर 2 वर्ष बाद मिश्रधन = \(1800 \times 1.1 = 1,980\text{ रुपये}\)।