A sum of money doubles itself at the compound interest x in 10 years. In how many years it will be four times at the same compound interest?

Correct option is B

​A sum of money doubles itself at the compound interest x in 10 years

$$\text{Amount} = P \cdot (1 + r)^t$$​​

Solution:

​$$P \cdot (1 + r)^{10} = 2P$$​​

Where:

Simplifying the equation:

​$$(1 + r)^{10} = 2$$

​​Now, we want to find the time it takes for the money to become 4 times the initial amount:

​​$$\ (1 + r)^t = P$$

​$$(1 + r)^t = 2^2$$

​$$\left[(1 + r)^{10}\right]^{\frac{t}{10}} = 2^2$$​​

$$t = 20$$​​​

Therefore, it will take 20 years for the money to become 4 times its initial amount at the same compound interest rate.