The compound interest on a certain sum for 2 years is Rs. 60.60 and simple interest is Rs. 60. Find the rate of interest.

Let the Principal be = P

$({\rm{S}}.{\rm{I}} = \frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}})$

$( \Rightarrow 60 = \frac{{{\rm{P}} \times {\rm{R}} \times 2}}{{100}})$

⇒ 6000 = 2PR

⇒ P × R = 3000

C.I = A - P 

$(= {\rm{P}}{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^2} - {\rm{P}})$

$(\Rightarrow 60.60 = \left( {\frac{{3000}}{{\rm{R}}}} \right) \times {\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^2} - \frac{{3000}}{R} = \left( {\frac{{3000}}{{\rm{R}}}} \right) \times \left( {1 + \frac{{{{\rm{R}}^2}}}{{10000}} + \frac{{2{\rm{R}}}}{{100}} - 1} \right))$

$(\Rightarrow 60.60 = \left( {\frac{{3000}}{{\rm{R}}}} \right) \times \left( {\frac{{{{\rm{R}}^2}}}{{10000}} + \frac{{2{\rm{R}}}}{{100}}} \right))$

⇒ 606 = 600 + 3R

∴ R = 6/3 = 2%

∴ 2% is the rate of interest.

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