At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?
Let $R \% p . a .$ be the required rate.
$A=4410$
$P=4000$
$n=2$ years
Now,$A=\mathrm{P}\left(1+\frac{R}{100}\right)^{n}$
$\Rightarrow 4410=4000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$
$\Rightarrow \frac{4410}{4000}=\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow \frac{441}{400}=\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow\left(\frac{21}{20}\right)^{2}=\left(1+\frac{R}{100}\right)^{2}$
$\Rightarrow \frac{21}{20}-1=\frac{R}{100}$
$\Rightarrow \frac{21-20}{20}=\frac{R}{100}$
$\Rightarrow \frac{1}{20}=\frac{R}{100}$
$\Rightarrow R=\left(\frac{1 \times 100}{20}\right)=5$
Hence, the required rate is $5 \%$ p.a.
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