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

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Question

(D) Let the principal amount be $P$.Given rate $R = 12 \frac{1}{2} \% = \frac{25}{2} \% = 12.5 \% = \frac{1}{8}$ per annum.Time $T = 2$ years.Compound

Vedclass · Accepted Answer

$480$

Vedclass · Answer

(D) Let the principal amount be $P$.Given rate $R = 12 \frac{1}{2} \% = \frac{25}{2} \% = 12.5 \% = \frac{1}{8}$ per annum.Time $T = 2$ years.Compound Interest ($C$.$I$.) formula: $C.I. = P \left[ \left(1 + \frac{R}{100} ight)^T - 1 ight]$.$510 = P \left[ \left(1 + \frac{1}{8} ight)^2 - 1 ight]$.$510 = P \left[ \left( \frac{9}{8} ight)^2 - 1 ight] = P \left[ \frac{81}{64} - 1 ight] = P \left( \frac{17}{64} ight)$.$P = \frac{510 	imes 64}{17} = 30 	imes 64 = ₹ 1920$.Now,Simple Interest ($S$.$I$.) = $\frac{P 	imes R 	imes T}{100} = \frac{1920 	imes 12.5 	imes 2}{100} = \frac{1920 	imes 25}{100} = 1920 	imes 0.25 = ₹ 480$.

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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