Find the ratio of S.I. and C.I. on a certain | vedclass

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(B) Let the principal amount be $P = 100$. Rate $R = 5 \%$ per annum and time $T = 2$ years. Simple Interest $(S.I.)$ $= \frac{P 	imes R 	imes T}{10

Vedclass · Accepted Answer

$40:41$

Vedclass · Answer

(B) Let the principal amount be $P = 100$. Rate $R = 5 \%$ per annum and time $T = 2$ years. Simple Interest $(S.I.)$ $= \frac{P 	imes R 	imes T}{100} = \frac{100 	imes 5 	imes 2}{100} = 10$. Compound Interest $(C.I.)$ $= P \left[ \left( 1 + \frac{R}{100} ight)^T - 1 ight] = 100 \left[ \left( 1 + \frac{5}{100} ight)^2 - 1 ight]$. $C.I. = 100 \left[ \left( \frac{105}{100} ight)^2 - 1 ight] = 100 \left[ \left( \frac{21}{20} ight)^2 - 1 ight] = 100 \left[ \frac{441}{400} - 1 ight] = 100 	imes \frac{41}{400} = \frac{41}{4} = 10.25$. Ratio of $S.I. : C.I. = 10 : 10.25 = 1000 : 1025$. Dividing both by $25$,we get $40 : 41$.

Find the ratio of $S.I.$ and $C.I.$ on a certain sum of money at $5 \%$ per annum for $2$ years.

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