A sum of money becomes ₹35,680 after 3 years and ₹53,520 after 6 years at a certain rate percentage p.a., interest compounded yearly. What is the compound interest on the same sum in the first case? (Your answer should be nearest to an integer)

₹11,893

We know ,

Amount = Principal × ( 1 + \(\frac{rate }{100}\) )t

53520 = 35680 × ( 1 + \(\frac{rate }{100}\) )³

( 1 + \(\frac{rate }{100}\) )³ = \(\frac{53520 }{35680}\)     ----(1)

Also ,

For first 3 years ,

35680 = Principal × ( 1 + \(\frac{rate }{100}\) )³        

( 1 + \(\frac{rate }{100}\) )3   = \(\frac{35680 }{Principal}\)   -----(2)

Equating equation 1 equals to 2

\(\frac{35680 }{Principal}\)  = \(\frac{53520 }{35680}\) 

Principal = 23786.6

Now , Compound interest of first 3 years = 35680 - 23786.6

= 11893.4

= 11893  ( approx )