Question

A sum of money lent out at compound interest at certain rate of interest becomes 2 times of itself in 3 years. In how many years, it will become 16 times of itself?

Answer 1

Given: A sum of money lent at compound interest becomes 2 times in 3 years.

Step-wise calculation:

Let the principal be (P) and the rate of interest be (r%).

After 3 years, amount (A = 2P),

So, `P(1 + r/100)^3 = 2P`

⇒ `(1 + r/100)^3 = 2`

We want to find the number of years (n) for the sum to become 16 times,

So, `P(1 + r/100)^n = 16P`

⇒ `(1 + r/100)^n = 16`

Since `(1 + r/100)^3 = 2`,

`(1 + r/100) = 2^(1/3)`

Therefore, `2^(n/3) = 16 = 2^4`

⇒ `n/3 = 4`

⇒ n = 12

The sum will become 16 times of itself in 12 years.