On a sum of money,the simple interest for 2 y | vedclass

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(D) Let the principal be $P$ and the rate of interest be $R \%$.Simple Interest $(S.I.)$ for $2$ years is given by:$S.I. = \frac{P 	imes R 	imes 2}{

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(D) Let the principal be $P$ and the rate of interest be $R \%$.Simple Interest $(S.I.)$ for $2$ years is given by:$S.I. = \frac{P 	imes R 	imes 2}{100} = 660$  --- $(1)$Compound Interest $(C.I.)$ for $2$ years is given by:$C.I. = P \left[ \left(1 + \frac{R}{100}ight)^2 - 1 ight] = 696.30$  --- $(2)$Dividing equation $(2)$ by equation $(1)$:$\frac{P \left[ \left(1 + \frac{R}{100}ight)^2 - 1 ight]}{\frac{P 	imes 2R}{100}} = \frac{696.30}{660}$$\frac{\frac{R^2}{10000} + \frac{2R}{100}}{\frac{2R}{100}} = 1.055$$\frac{R}{200} + 1 = 1.055$$\frac{R}{200} = 0.055$$R = 0.055 	imes 200 = 11$Thus,the rate of interest is $11 \%$.

On a sum of money,the simple interest for $2$ years is ₹ $660$,while the compound interest is ₹ $696.30$,the rate of interest being the same in both the cases. The rate of interest (in $\%$) is

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