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# Swati borrowed Rs 40960 from a bank to buy a piece of land. If the bank charges $12\frac{1}{2}%$ per annum, compounded half-yearly, what amount will she have to pay after $1\frac{1}{2}$ years? Also, find the interest paid by her.

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## $\mathrm{Principal},P\mathit{}=\mathrm{Rs}.40960\phantom{\rule{0ex}{0ex}}\mathrm{Annual}\mathrm{rate}\mathrm{of}\mathrm{interest},R\mathit{}=\frac{25}{2}%\phantom{\rule{0ex}{0ex}}\mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{half}\mathrm{year}=\frac{25}{4}%\phantom{\rule{0ex}{0ex}}\mathrm{Time},n=1\frac{1}{2}\mathrm{years}=3\mathrm{half}\mathrm{years}\phantom{\rule{0ex}{0ex}}\mathrm{Then}\mathrm{the}\mathrm{amount}\mathrm{with}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{is}\mathrm{given}\mathrm{by}\phantom{\rule{0ex}{0ex}}A=P×{\left(1+\frac{R}{100}\right)}^{n}\phantom{\rule{0ex}{0ex}}=40960×{\left(1+\frac{25}{100×4}\right)}^{3}\phantom{\rule{0ex}{0ex}}=40960×{\left(\frac{400+25}{400}\right)}^{3}\phantom{\rule{0ex}{0ex}}=40960×{\left(\frac{425}{400}\right)}^{3}\phantom{\rule{0ex}{0ex}}=40960×\left(\frac{17}{16}\right)×\left(\frac{17}{16}\right)×\left(\frac{17}{16}\right)\phantom{\rule{0ex}{0ex}}=\left(10×17×17×17\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}49130\phantom{\rule{0ex}{0ex}}{\mathrm{Therefore}}{,}{}{\mathrm{compound}}{}{\mathrm{interest}}{}{=}{}{\mathrm{amount}}{}{-}{}{\mathrm{principal}}{=}{\mathrm{Rs}}{}{\left(}{49130}{-}{}{40960}{\right)}{}{=}{}{\mathrm{Rs}}{}{8170}\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{Swati}\mathrm{has}\mathrm{to}\mathrm{pay}\mathrm{Rs}.49130,\mathrm{which}\mathrm{includes}\mathrm{an}\mathrm{interest}\mathrm{of}\mathrm{Rs}.8170,\mathrm{to}\mathrm{the}\mathrm{bank}\mathrm{after}1\frac{1}{2}\mathrm{years}.$  Suggest Corrections  0      Similar questions  Related Videos   Simple and Compound Interest
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