A certain amount of money becomes thrice in 5 years at compound interest. How many years it will take to become 9 times?

Correct option is B

Given:
Principal amount becomes 3 times in 5 years at compound interest.
Formula Used:
Compound Interest Formula:
A =$$P \left(1 + \frac{r}{100}\right)^n$$​​
Where:
A = Amount after n years
P = Principal amount
r  = Annual interest rate (%)

n = Time period (years)
Solution:
$$3P = P \left(1 + \frac{r}{100}\right)^5$$​
​$$\left(1 + \frac{r}{100}\right)^5 = 3 \quad \text{(Equation 1)}$$​

$$9P = P \left(1 + \frac{r}{100}\right)^n$$​

​$$\left(1 + \frac{r}{100}\right)^n = 9 \quad \text{(Equation 2)}$$​
​$$\left(1 + \frac{r}{100}\right)^n = \left(\left(1 + \frac{r}{100}\right)^5\right)^2$$​​

$$\left(1 + \frac{r}{100}\right)^n = \left(1 + \frac{r}{100}\right)^{10}$$​

Compare exponents:
n = 10 years
Alternate Method:
If money becomes k times in t years, it becomes $$k^m$$​ times in $$m \times t$$​ years.
Given growth pattern:
3 times growth in 5 years
Determine growth factor for 9 = $$3^2$$​ times:
Time required = 2 $$\times 5$$​ = 10 years