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)
Answer & explanation
Correct answer: option 1
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 )