The compound interest on a certain sum for 2 years is Rs. 900 and the simple interest is Rs. 800. The difference between compound and simpl…

The difference between C.I. and S.I. for 2 years = S.I. on the interest of first year

⇒ S.I. for first year = Rs. 400

⇒ The S.I. on interest of first year = C.I. – S.I. = 900 – 800 = Rs. 100

⇒ Interest on Rs.400 for 1 year = Rs. 100

⇒ Interest on Rs.100 for 1 year = x

⇒ i.e, x = [(100 × 100)/400] = Rs. 25

⇒ Thus the rate of interest = 25%

$(\Rightarrow {\rm{Principal\;amount}} = {\rm{}}\frac{{\left( {100 \times {\rm{S}}.{\rm{I}}} \right){\rm{\;}}}}{{RT}})$

⇒ Principal amount = (100 × 800)/(2 × 25)

⇒ Principal amount = Rs. 1600

⇒ S.I. for 3 years = (1600 × 3 × 25)/100

⇒ S.I. for 3 years = Rs. 1200

⇒ C.I. for 3 years = 1600[(1 + 0.25) 3 – 1]

⇒ C.I. for 3 years = Rs. 1525

⇒ Difference between C.I. and S.I. for 3 years = 1525 – 1200 = Rs. 325

∴ Difference between C.I. and S.I. for 3 years = Rs. 325