The difference between the compound interest | vedclass

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(D) Let the rate of interest be $R \%$ per annum.The formula for the difference between compound interest $(C.I.)$ and simple interest $(S.I.)$ for $2

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$15$

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(D) Let the rate of interest be $R \%$ per annum.The formula for the difference between compound interest $(C.I.)$ and simple interest $(S.I.)$ for $2$ years is given by:Difference $= P 	imes \left(\frac{R}{100}ight)^2$Given:Principal $(P)$ $= ₹ 18000$Difference $= ₹ 405$Time $(T)$ $= 2$ yearsSubstituting the values into the formula:$405 = 18000 	imes \left(\frac{R}{100}ight)^2$$\left(\frac{R}{100}ight)^2 = \frac{405}{18000}$$\left(\frac{R}{100}ight)^2 = \frac{81}{3600}$Taking the square root on both sides:$\frac{R}{100} = \sqrt{\frac{81}{3600}}$$\frac{R}{100} = \frac{9}{60}$$R = \frac{9}{60} 	imes 100$$R = 15$Therefore,the rate of interest is $15 \%$ per annum.

The difference between the compound interest and the simple interest accrued on an amount of ₹ $18000$ in $2$ years was ₹ $405$. What was the rate of interest per cent per annum?

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