Question

Calculate the compound interest on 4000 at 5% p.a. for 1 year , interest being compounded half yearly.

Answer 1

AnswEr :

Rs.202.5

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

• Principal,[P] = Rs.4000
• Rate,[R] = 5% p.a.
• Time,[n] = 1 years.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The compound Interest.

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

Formula use : (Compounded half - yearly)

$\bf{\boxed{\sf{A=P\bigg(1+\frac{R}{2*100} \bigg)^{2n} }}}}$

$\mapsto\sf{A=4000\bigg(1+\cancel{\dfrac{5}{200}} \bigg)^{2\times 1} }\\\\\\\mapsto\sf{A=4000\bigg(1+\dfrac{1}{40} \bigg)^{2} }\\\\\\\mapsto\sf{A=4000\bigg(\dfrac{40+1}{40}\bigg)^{2} }\\\\\\\mapsto\sf{A=4000\times \dfrac{41}{40} \times \dfrac{41}{40} }\\\\\\\mapsto\sf{A=40\cancel{00}\times \dfrac{1681}{16\cancel{00}} }\\\\\\\mapsto\sf{A=40\times \cancel{\dfrac{1681}{16} }}\\\\\\\mapsto\sf{A=Rs.(40\times105.06)}\\\\\\\mapsto\sf{\red{A=Rs.4202.5}}$

Now;

We know that compound Interest :

$\leadsto\sf{C.I.=A-P}\\\\\leadsto\sf{C.I.=Rs.4202.5-Rs.4000}\\\\\leadsto\sf{\red{C.I.=Rs.202.5}}$

Thus;

The compound Interest (C.I.) is Rs.202.5 .

Answer 2

$\huge\orange{\underline{\underline{\blue{\mathtt{Question}}}}}$

Calculate the compound interest on 4000 at 5% p.a. for 1 year , interest being compounded half yearly.

$\huge\orange{\underline{\underline{\blue{\mathtt{To\;find}}}}}$

Calculate the compound interest being compounded half yearly

$\huge\orange{\underline{\underline{\blue{\mathtt{Solution}}}}}$

• Principal = Rs.4000
• Rate = 5%
• Time = 1year

$\implies\sf A=P\left(1+\Large\frac{R}{200}\right)^{2n}$

$\implies\sf A=4000\left(1+\Large\frac{5}{200}\right)^{2\times{1}}$

$\implies\sf A=4000\left(1+\Large\frac{1}{40}\right)^2$

$\implies\sf A=4000\left(\Large\frac{40+1}{40}\right)^2$

$\implies\sf A=4000\times\frac{41}{40}\times\frac{41}{40}$

$\implies\sf A=\Large\frac{4000×41×41}{40×40}$

$\implies\sf A=\Large\cancel\frac{8405}{2}=Rs.4202.5$

Now

$\sf Compound\:interest=Amount-Principal$

$\sf Compound\:inetrest = Rs.4202.5 - Rs.4000$

$\sf Compound\:interest= Rs.202 .5$

$\large{\boxed{\bf{\red{C.I = Rs.202.5}}}}$