What is the difference between the compound i | vedclass

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Question

Difference in C.I. $=5000\left[\left(1+\frac{2}{100}\right)^{3}-1\right]-5000\left[\left(1+\frac{4}{100}\right)\left(1+\frac{2}{100}\right)-1\right]$

Vedclass · Accepted Answer

$2.04$

Vedclass · Answer

Difference in C.I. $=5000\left[\left(1+\frac{2}{100}ight)^{3}-1ight]-5000\left[\left(1+\frac{4}{100}ight)\left(1+\frac{2}{100}ight)-1ight]$

$=5000\left[\left\{\left(\frac{51}{50}ight)^{3}-1ight\}-\left(\frac{26}{25} 	imes \frac{51}{50}-1ight)ight]$

$=5000\left[\left(\frac{51^{3}-50^{3}}{50^{3}}ight)-\frac{\left(13 	imes 51-25^{2}ight)}{25^{2}}ight]$

$=5000\left[\frac{51^{2}+50^{2}+51(50)}{50^{3}}-\frac{(663-625)}{25^{2}}ight]$

$=5000\left[\frac{2601+2500+2550}{50^{3}}-\frac{38}{25^{2}}ight]=5000\left[\frac{7651}{50^{3}}-\frac{38}{25^{2}}ight]$

$=\frac{5000}{50^{3}}[7651-38 	imes 4 	imes 50]=\frac{2}{50}[7651-7600]$

$=\frac{2}{50} 	imes 51=₹ 2.04$

What is the difference between the compound interests (In ₹ ) on ₹ $5000$ for $1 \frac{1}{2}$ years at $4 \%$ per annum compounded yearly end half-yearly?

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