Question

At what rate percent will 2000rs amount to 2315.25rs in 3 years at compound interest?
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Answer 1

S O L U T I O N :

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

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

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

Using formula of the compounded annually;

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

A/q

$\mapsto\tt{2315.25 =2000\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{2315.25}{2000} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{2315.25 \times 100}{2000\times 100} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{231525}{200000} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\cancel{\dfrac{231525}{200000}} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\cancel{\dfrac{46305}{40000}} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{9261}{8000} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{3\sqrt{\dfrac{9261}{8000} }=1+\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{21}{20} =1+\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{21}{20}-1 =\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{21-20}{20} =\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{1}{20} =\dfrac{R}{100} }$

$\mapsto\tt{20R= 100\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{R = \cancel{100/20}}$

$\mapsto\bf{R = 5\:\%}$

Thus,

The rate of the compound Interest will be 5% .

Answer 2

Answer:

hlo

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