A sum of money doubles itself at a compound interest in 15 years. In how many years will it become 8 times the original amount?

Correct option is B

Given:

A sum doubles at compound interest in 15 years

Need to find the time it will take to become 8 times the original amount

Concept Used:

​$$A = P \left(1 + r\right)^t$$​​

Solution:
If amount doubles in 15 years:

​$$2P = P(1 + r)^{15}$$​

​$$(1 + r)^{15} = 2$$​

Now we want:

​$$8P = P(1 + r)^T$$​

​$$(1 + r)^T = 8$$​

​$$(1 + r)^T = 2^3$$​​
From powers of 2:

​$$T = 15 \times 3 = 45 \text{ years}$$​

The amount will become 8 times in 45 years.

Alternate Method:

If the principal doubles in 15 years, then:

It becomes 2 times in 15 years.

It becomes 2 $$\times$$​ 2 = 4 times in 15 + 15 = 30 years.

It becomes 2$$\times$$ 2$$\times$$ 2 = 8 times in 15 + 15 + 15 = 45 years.​​