The compound interest on a certain sum for 2 years is Rs. 60.60 and si

1.	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.1). 1%2). 2%3). 3%4). 4%
Answer» 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.

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.1). 1%2). 2%3). 3%4). 4%

Answer»

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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