Question:
A sum of money doubles itself in 5 years at a certain rate of compound interest per annum. In how many years will it become 16 times of itself at the same rate?
एक निश्चित वार्षिक चक्रवृद्धि ब्याज दर पर कोई धनराशि 5 वर्षों में दोगुनी हो जाती है। समान दर पर यह कितने वर्षों में स्वयं की 16 गुनी हो जाएगी?
Options:
- 20 years
- 25 years
- 15 years
- 30 years
- 20 वर्ष
- 25 वर्ष
- 15 वर्ष
- 30 वर्ष
Correct Answer: a)
Explanation:
Under compound interest, if a principal becomes \(k\) times in \(T\) years, it becomes \(k^n\) times in \(n \times T\) years.
Here, \(k = 2\) and \(T = 5\) years.
We want it to become 16 times: \(16 = 2^4 \implies n = 4\).
Required time = \(4 \times 5 = 20\) years.
Here, \(k = 2\) and \(T = 5\) years.
We want it to become 16 times: \(16 = 2^4 \implies n = 4\).
Required time = \(4 \times 5 = 20\) years.
चक्रवृद्धि ब्याज में यदि कोई राशि \(T\) वर्षों में \(k\) गुनी होती है, तो वह \(n \times T\) वर्षों में \(k^n\) गुनी हो जाती है।
यहाँ \(16 = 2^4\), अतः \(n = 4\)।
कुल समय = \(4 \times 5 = 20\) वर्ष।
यहाँ \(16 = 2^4\), अतः \(n = 4\)।
कुल समय = \(4 \times 5 = 20\) वर्ष।