The difference of compound interest (In ₹) on | vedclass

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Question

(a) When compounded half-yearly:

Here, $P=800, R=20$ and $t=1$

$	herefore \quad CI =P\left[\left(1+\frac{R}{100 	imes 2}ight)^{2 	imes t}-1

Vedclass · Accepted Answer

$4.40$

Vedclass · Answer

(a) When compounded half-yearly:

Here, $P=800, R=20$ and $t=1$

$	herefore \quad CI =P\left[\left(1+\frac{R}{100 	imes 2}ight)^{2 	imes t}-1ight]$

$=800\left[\left(1+\frac{20}{100 	imes 2}ight)^{2 	imes 1}-1ight]$

$=800\left[\left(\frac{11}{10}ight)^{2}-1ight]=\frac{800 	imes 21}{10 	imes 10}=₹ 168$

When compounded quarterly:

$\begin{aligned} 	ext { Here, } P &=8000, R=20 	ext { and } t=1 \ 	herefore \quad C I &=P\left[\left(1+\frac{R}{100 	imes 4}ight)^{4 	imes t}-1ight] \ &=800\left[\left(1+\frac{20}{100 	imes 4}ight)^{4 	imes 1}-1ight] \ &=800\left[\left(\frac{21}{20}ight)^{4}-1ight]=\frac{800 	imes 34481}{20 	imes 20 	imes 20 	imes 20} \ &=₹ 172.40 \end{aligned}$

$	herefore \quad$ Difference $=₹(172.40-168)=₹ 4.40$

The difference of compound interest (In ₹) on ₹ $800$ for $1$ year at $20 \%$ per annum when compounded half-yearly and quarterly is

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