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A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times of itself at the same rate of interest in
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- 20 years
- 10 years
- 12 years
- 15 years
Correct Option: D
Here , Time = 5 years
Let principal be P and Amount = 2P
Using the given formula ,
| A = P |  | 1 + |  | n | |
| 100 |
| ⇒ 2P = P | | 1 + | | 5 | |
| 100 |
On cubing both sides,
| 23 = | | 1 + | | 5 × 3 | |
| 100 |
| ⇒ 8 = 1 | | 1 + | | 15 | |
| 100 |
∴ Required time = 15 years
Second Method to solve this question :
p = 2, n1 = 5, q = 8, n2 = ?
Here, p 1/n1 = q1/n2
(2)1/5 = (8)1/n2
21/5 = (2)3/n2
| ⇒ | = | ||
| 5 | n2 |
∴ n2 = 15
