A sum of money lent at compound interest yields Rs 100 at the end of first year and Rs 105 at the end of 2nd year .The rate % per annum is?

$P(1+\frac{r}{100})=100;...\left(1\right)\phantom{\rule{0ex}{0ex}}P(1+\frac{r}{100}{)}^{2}=105;...(2)\phantom{\rule{0ex}{0ex}}Dividing(2)by1,\phantom{\rule{0ex}{0ex}}1+\frac{r}{100}=1.05;\phantom{\rule{0ex}{0ex}}\frac{r}{100}=0.05;\phantom{\rule{0ex}{0ex}}r=5\%\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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