Question

What sum of money will amount to 22050 in 2 years and 23152.50 in 3 years at 5%
per annum compound interest?​

Answer 1

S O L U T I O N :

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

• Principal, (P) = ?
• Amount, (A) = Rs.22050
• Time, (T) = 2 years
• Amount,(A) = Rs.23152.50
• Time, (T) = 3 years
• Rate, (R) = 5% p.a.

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

The sum of the money.

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

We know that formula of the compounded annually :

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

For 2 years :

$\longrightarrow\sf{22050=P\bigg(1+\cancel{\dfrac{5}{100}}\bigg)^{2} }\\\\\\\longrightarrow\sf{22050=P\bigg(1+\dfrac{1}{20} \bigg)^{2} }\\\\\\\longrightarrow\sf{22050=P\bigg(\dfrac{20+1}{20} \bigg)^{2} }\\\\\\\longrightarrow\sf{22050=P\bigg(\dfrac{21}{20} \bigg)^{2} }\\\\\\\longrightarrow\sf{22050=P\times \dfrac{21}{20} \times \dfrac{21}{20} }\\\\\\\longrightarrow\sf{P=\dfrac{\cancel{22050} \times 20\times 20}{\cancel{441}} }\\\\\\\longrightarrow\sf{P=Rs.(50\times 400)}$

$\longrightarrow\bf{P=Rs.20000}$

For 3 years :

$\longrightarrow\sf{23152.50=P\bigg(1+\cancel{\dfrac{5}{100}}\bigg)^{3} }\\\\\\\longrightarrow\sf{23152.50=P\bigg(1+\dfrac{1}{20} \bigg)^{3} }\\\\\\\longrightarrow\sf{23152.50=P\bigg(\dfrac{20+1}{20} \bigg)^{3} }\\\\\\\longrightarrow\sf{23152.50=P\bigg(\dfrac{21}{20} \bigg)^{3} }\\\\\\\longrightarrow\sf{23152.50=P\times \dfrac{21}{20} \times \dfrac{21}{20} \times\dfrac{21}{20}}\\\\\\\longrightarrow\sf{P=\dfrac{\cancel{23152.50} \times 20\times 20\times 20}{\cancel{441}\times 21}}$

$\longrightarrow\sf{P=\dfrac{52.5\times 20\times 20\times 20}{21} }\\\\\\\longrightarrow\sf{P=\cancel{\dfrac{420000}{21} }}\\\\\\\longrightarrow\bf{P=Rs.20000}$

Thus;

The Total sum of the money will be Rs.20000 + Rs.20000 = Rs.40000 .