Question

At what rate of interest per annum will 800 amount to 882 in 1 year when compounded half-yearly?​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Principal, (P) = Rs.800
• Amount, (A) = Rs.882
• Time, (n) = 1 years

$\underline{\bf{Explanation\::}}$

As we know that formula of the compounded half-yearly;

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R/2}{100} \bigg)^{2n}}}$

A/q

$\mapsto\tt{882 = 800\bigg(1+\dfrac{R}{2\times 100} \bigg)^{(2\times 1)}}$

$\mapsto\tt{\cancel{\dfrac{882}{800}} =\bigg(1+\dfrac{R}{2\times 100} \bigg)^{2}}$

$\mapsto\tt{\dfrac{441}{400}= \bigg(1+\dfrac{R}{ 200} \bigg)^{2}}$

$\mapsto\tt{\sqrt{\dfrac{441}{400} } = 1+\dfrac{R}{ 200} }$

$\mapsto\tt{\dfrac{21}{20}= 1+\dfrac{R}{ 200}}$

$\mapsto\tt{\dfrac{21}{20}-1= \dfrac{R}{ 200}}$

$\mapsto\tt{\dfrac{21-20}{20}= \dfrac{R}{ 200}}$

$\mapsto\tt{\dfrac{1}{20}= \dfrac{R}{ 200}}$

$\mapsto\tt{20R=200\:\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{R=\cancel{200/20}}$

$\mapsto\bf{R=10\:\%}$

Thus;

The rate of the Interest will be 10% .