A sum of ₹7,000 deposited at compound interest becomes triple of itself after 4 years. How much will the amount be after 12 years?

Solution

A sum of ₹7,000 deposited at compound interest becomes triple of itself after 4 years.

So money after 4 years = $$7000\times3$$

= 21000

$$interest\ +\ principal\ =\ principal\left(1+\frac{rate}{100}\right)^{time}$$

$$21000=\ 7000\left(1+\frac{rate}{100}\right)^4$$

$$3=\ \left(1+\frac{rate}{100}\right)^4$$

Now apply cube in the above equation.
$$3^3=\ \left[\left(1+\frac{rate}{100}\right)^4\right]^3$$

$$27=(1+\frac{rate}{100})^{4\times3}$$
$$27=\ \left(1+\frac{rate}{100}\right)^{12}$$

So from the above equation, we can say that after 12 years money will be 27 times itself.

Hence money after 12 years = $$27\times7000$$

= 189000