Question:
The amount at the end of the 3rd and 4th years on a certain principal at compound interest is Rs. 13,310 and Rs. 14,641 respectively. Find the principal.
चक्रवृद्धि ब्याज पर एक निश्चित मूलधन पर तीसरे और चौथे वर्ष के अंत में मिश्रधन क्रमशः 13,310 रुपये और 14,641 रुपये है। मूलधन ज्ञात कीजिए।
Options:
- Rs. 10,000
- Rs. 11,000
- Rs. 12,100
- Rs. 9,000
- 10,000 रुपये
- 11,000 रुपये
- 12,100 रुपये
- 9,000 रुपये
Correct Answer: a)
Explanation:
Interest for the 4th year = \(14641 – 13310 = \text{Rs. } 1331\).
Rate of interest \(r = \dfrac{1331}{13310} \times 100 = 10\%\).
Amount after 3 years \(A_3 = P\left(1 + \dfrac{10}{100}\right)^3 = 1.331 P = 13310\).
\(P = \dfrac{13310}{1.331} = \text{Rs. } 10,000\).
चौथे वर्ष का ब्याज = \(14641 – 13310 = 1331\) रुपये।
ब्याज दर \(r = \dfrac{1331}{13310} \times 100 = 10\%\)।
3 वर्ष बाद मिश्रधन \(A_3 = P(1.1)^3 = 1.331 P = 13310\)।
\(P = \dfrac{13310}{1.331} = 10,000\) रुपये।