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Question

(A) Given,Simple Interest ($S$.$I$.) = ₹ $50$,Time $(T)$ = $2$ years,Rate $(R)$ = $5 \%$.Using the formula for Simple Interest: $S.I. = \frac{P 	imes

Vedclass · Accepted Answer

$51.25$

Vedclass · Answer

(A) Given,Simple Interest ($S$.$I$.) = ₹ $50$,Time $(T)$ = $2$ years,Rate $(R)$ = $5 \%$.Using the formula for Simple Interest: $S.I. = \frac{P 	imes R 	imes T}{100}$.$50 = \frac{P 	imes 5 	imes 2}{100} \implies 50 = \frac{10P}{100} \implies 50 = \frac{P}{10}$.Therefore,Principal $(P)$ = ₹ $500$.Now,calculating Compound Interest ($C$.$I$.) for the same principal,rate,and time:$C.I. = P \left[ \left( 1 + \frac{R}{100} ight)^T - 1 ight]$.$C.I. = 500 \left[ \left( 1 + \frac{5}{100} ight)^2 - 1 ight] = 500 \left[ \left( \frac{21}{20} ight)^2 - 1 ight]$.$C.I. = 500 \left[ \frac{441}{400} - 1 ight] = 500 	imes \frac{41}{400}$.$C.I. = \frac{5 	imes 41}{4} = \frac{205}{4} = ₹ 51.25$.

If the simple interest on a sum of money for $2$ years at $5 \%$ per annum is ₹ $50$,what is the compound interest (in ₹) on the same sum at the same rate and for the same time?

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