Question

at what rate per cent will a sum of ₹18750 amount to ₹21870 in 2 years compounded annually?​

Answer 1

$\bf \underline{Given} :$ ↴

$\sf \implies Principal = Rs. \: 18750$

$\sf \implies Amount = Rs. \: 21870$

$\sf \implies Time = 2 \: years$

$\bf \underline{To \: find} :$ ↴

$\sf \implies Rate \: of \: interest$

$\bf \underline{\underline{Solution }}$

$\sf As \: we \: know \: that,$

$\sf \implies\boxed{ \pink{ \sf Amount = P \bigg(1+ \dfrac{R}{100} \bigg)^{n}}}$

$\sf Putting \: the \: values,$

$\sf \implies \sf 21870 = 18750 \bigg(1+ \dfrac{R}{100} \bigg)^{2}$

$\sf \implies \cancel\dfrac{21870}{18750} = \bigg(1+ \dfrac{R}{100} \bigg)^{2}$

$\sf \implies \dfrac{729}{625} = \bigg(1+ \dfrac{R}{100} \bigg)^{2}$

$\sf \implies \sqrt{ \dfrac{729}{625} } =1+ \dfrac{R}{100}$

$\sf \implies \dfrac{27 \times 27}{25 \times 25} = 1+ \dfrac{R}{100}$

$\sf \implies \dfrac{27}{25} = 1+ \dfrac{R}{100}$

$\sf \implies \dfrac{27}{25} - 1 = \dfrac{R}{100}$

$\sf \implies \dfrac{27 - 25}{25} = \dfrac{R}{100}$

$\sf \implies \dfrac{2}{\!\!\!\not2\!\!\!\not5} = \dfrac{R}{\!\!\!\not1\!\!\!\not0\!\!\!\not0}$

$\sf \implies 2 = \dfrac{R }{4}$

$\sf \implies 2 \times 4 = R$

$\sf \implies 8 = R$

$\underline{ \boxed{ \sf \pink{ Hence, rate \: of \: interest = 8 \: \% }}}$