If the compound interest on a sum for 2 years | vedclass

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(D) Let the principal be $P$. The rate of interest $R = 12 \frac{1}{2} \% = 12.5 \% = \frac{25}{2} \%$. The time $T = 2$ years.The formula for compoun

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$480$

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(D) Let the principal be $P$. The rate of interest $R = 12 \frac{1}{2} \% = 12.5 \% = \frac{25}{2} \%$. The time $T = 2$ years.The formula for compound interest is $CI = P \left[ \left( 1 + \frac{R}{100} ight)^T - 1 ight]$.Given $CI = 510$,we have:$510 = P \left[ \left( 1 + \frac{25/2}{100} ight)^2 - 1 ight]$$510 = P \left[ \left( 1 + \frac{1}{8} ight)^2 - 1 ight]$$510 = P \left[ \left( \frac{9}{8} ight)^2 - 1 ight]$$510 = P \left( \frac{81}{64} - 1 ight) = P \left( \frac{17}{64} ight)$$P = \frac{510 	imes 64}{17} = 30 	imes 64 = 1920$.Now,calculate the simple interest $(SI)$ for the same principal,rate,and time:$SI = \frac{P 	imes R 	imes T}{100} = \frac{1920 	imes (25/2) 	imes 2}{100} = \frac{1920 	imes 25}{100} = 19.2 	imes 25 = 480$.Thus,the simple interest is ₹ $480$.

If the compound interest on a sum for $2$ years at $12 \frac{1}{2} \%$ per annum is ₹ $510$,the simple interest (in ₹) on the same sum at the same rate for the same period of time is

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