Question

At what rate percent will 2000 amount to 2315.25 in 3 years at compound interest

Answer 1

Answer:

5%

Step-by-step explanation:

for justification what's app 9467169711

Answer 2

S O L U T I O N :

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

• Amount (A) = Rs.2315.25
• Principal (P) = Rs.2000
• Time (T) = 3 years

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

The rate of the compound Interest.

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

We know that formula of the Compounded annually :

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

A/q

$\longrightarrow\sf{2315.25=2000\bigg(1+\dfrac{R}{100} \bigg)^{3} }\\\\\\\longrightarrow\sf{\dfrac{2315.25}{2000} =\bigg(1+\dfrac{R}{100} \bigg)^{3} }\\\\\\\longrightarrow\sf{\dfrac{2315.25\times 100}{2000\times 100}=\bigg(1+\dfrac{R}{100} \bigg)^{3} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{231525}{200000} }=\bigg(1+\dfrac{R}{100} \bigg)^{3} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{46305}{40000}} =\bigg(1+\dfrac{R}{100} \bigg)^{3} }$

$\longrightarrow\sf{\dfrac{9261}{8000}=\bigg(1+\dfrac{R}{100} \bigg)^{3} }\\\\\\\longrightarrow\sf{3\sqrt{\dfrac{9261}{8000} } =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} -1=\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21-20}{20} =\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{1}{20} =\dfrac{R}{100} }\\\\\\\longrightarrow\sf{20R=100\:\:\underbrace{\sf{Cross-multiplication}}}}$

$\longrightarrow\sf{R=\cancel{\dfrac{100}{20} }}\\\\\\\longrightarrow\bf{R=5\%}$

Thus;

The rate of the compound Interest will be 5% .