Question

find the compund interest on 1000 at the rate of 10% per annum from 18 months when intereste in compound in half year?​

Answer 1

$\bf \underline{Note} :$ ↴

When interest is compounded half yearly, then rate of interest would be halfed and time (n) will be doubled that is 2n.

$\bf \underline{Given} :$ ↴

$\sf \implies Principal = Rs. 1000$

$\sf \implies Rate \: of \: interest = \dfrac{10}{2} = 5 \: \%$

$\sf \implies Time = 18 \: months = \dfrac{3}{2} \: years \: = \dfrac{3}{2} \times 2 = 3 \: years.$

$\bf \underline{To \: find} :$ ↴

$\sf \implies Compound \: Interest = \:?$

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

$\sf First \:of \:all \:we \:have\: to\: find \:the \:amount,$

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

$\sf \implies{\sf 1000 \: \bigg(\: 1 + \dfrac{5}{100} \bigg ) ^{3} }$

$\sf \implies{\sf 1000 \: \bigg(\: 1 + \dfrac{1}{20} \bigg ) ^{3} }$

$\sf \implies{\sf 1000 \bigg( \dfrac{20+1}{20} \bigg ) ^{3} }$

$\sf \implies{\sf 1000 \bigg( \dfrac{21}{20} \bigg ) ^{3} }$

$\sf \implies{\sf 1000\times \dfrac{9261}{8000} }$

$\sf \implies{\sf \dfrac{9261}{8} }$

$\sf \implies{\sf 1157.625 }$

$\sf \red{ \implies Amount = Rs.\: 1157.625}$

$\sf Now, we\: will\: find\: the\: compound\: interest,$

$\sf \implies{ \boxed{ \purple{ \sf Compound \:interest = Amount - Principal }}}$

$\sf \implies 1157.625 - 1000$

$\red{\sf \implies Compound \:interest = Rs. \:157.625}$

Hence, Compound interest on 1000 at the rate of 10% is Rs. 157.625.