A sum invested at a certain rate of interest per annum, compounded annually, amounts to ₹14,400 in 2 years and to ₹25,920 in 4 years. What is the sum invested?

₹8,000

Formula used here is -

Amount = P$(1 \;+\; \frac{R}{100})^t$

In 1st case,

14400 = P( 1 + \(\frac{R}{100}\))²

ATQ,

In 2nd case,

25920 = P( 1 + \(\frac{R}{100}\))⁴

25920 = P (\(\frac{14400}{P}\))²

On solving ,

P = 8000

So, Initial sum = Rs. 8000