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A sum of money invested at compound interest doubles itself in 6 years. At the same rate of interest it will amount to eight times of itself in :
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- 15 years
- 12 years
- 18 years
- 10 years
Correct Option: C
Here , Time = 6 years , Rate = r%
Let the sum be P. Then,
From the question ,
| 2P = P |  | 1 + |  | 6 | |
| 100 |
| ⇒ 2 = | | 1 + | | 6 | |
| 100 |
Cubing on both sides, we get
| 8 = |  | | 1 + | | 6 |  | 3 | |
| 100 |
| ⇒ 8 = | | 1 + | | 18 | |
| 100 |
Multiplying by P both sides ,
| ⇒ 8P = P | | 1 + | | 18 | |
| 100 |
∴ The sum will be 8 times in 18 years. i.e., Time = 18 years
Second Method to find required answer :
Here, m = 2, t = 6 years
It will becomes 8 times of itself = 23 times of itself in t × n years = 6 × 3 = 18 years
