PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018
Answer
45 years
Explanation
In compound interest, a sum of money grows exponentially by the same multiplying factor over equal intervals of time. The problem states that the money doubles (becomes 2 times) in 15 years. We need to find the time it takes to become 8 times. We can write 8 as a power of 2: 8 = 2³. According to the shortcut trick for compound interest, multiply the time period by this power. Therefore, required time = 15 years × 3 = 45 years.
Key Points
- > Compound interest follows an exponential growth pattern.
- > Rule: If money becomes 'n' times in 't' years, it will become 'n^m' times in 'm × t' years.
- > Given: money becomes 2 times in 15 years.
- > Target: 8 times. We know 8 = 2³.
- > Therefore, the power (m) is 3.
- > Required time = 15 × 3 = 45 years.
Additional Information
Compound Interest Time Table (Doubling)
| Multiplication Factor | Power of 2 | Total Time Required |
|---|---|---|
| 2 times (Doubles) | 2¹ | 15 years |
| 4 times | 2² | 15 × 2 = 30 years |
| 8 times | 2³ | 15 × 3 = 45 years |
| 16 times | 2⁴ | 15 × 4 = 60 years |
Memory Tips
- The Power Multiplier Rule: For Compound Interest, write the target multiple as a base of the initial multiple. $8 = 2^3$. Multiply the time (15) by the exponent (3). $15 \times 3 = 45$.