Question

sudhir invested 10000 in a finnce company and received 14,641 after 4 years, find the rate of
interest per cent per annum compounded annually.
​

Answer 1

$\underline{ \underline{\sf{Given}}}$

Sudhir invested 10000 in a finnce company and received 14,641 after 4 years.

$\underline{ \underline{ \sf{To \: find \: out}}}$

Find the rate of interest per cent per annum compounded annually.

$\underline{ \underline{ \sf{Formula \: used}}}$

$\boxed{ \sf{A = P(1 + \frac{r}{100} ) {}^{n} }}$

$\underline{ \underline{ \sf{Solution}}}$

We have,

• Principal,P = 10000

• Amount,A = 14641

• Time, n = 4 years

$\sf{A = P(1 + \frac{r}{100} ) {}^{n}}$

★ Substituting the values in the above formula,we get:

$\implies \sf{ 14641 = 10000 \: (1 + \dfrac{r}{100} ) {}^{4} }$

$\implies \sf{(1 + \dfrac{r}{100}) {}^{4} = \frac{14641}{10000} }$

$\implies \sf{1 + \dfrac{r}{100} = \sqrt[4]{ \dfrac{14641}{10000} } }$

$\implies \sf{1 + \dfrac{r}{100} = \dfrac{11}{10} }$

$\implies \sf{ \dfrac{r}{100} = \dfrac{11}{10} - 1 }$

$\implies \sf{ \dfrac{r}{100} = \dfrac{11 - 10}{10} }$

$\implies \sf{ \dfrac{r}{100} = \dfrac{1}{10} }$

$\implies \sf{r = \dfrac{1}{10} \times 100 }$

$\implies \sf{ \therefore \: r = 10\% \: p.a}$

Hence, the rate of interest is 10% p.a .

Answer 2

Given ,

" Sudhir invested 10000 in a finace company and received 14,641

after 4 years "

$\underbrace{\bf{A=P(1+\dfrac{r}{100})^n}}$

where ,

• A denotes Amount
• P denotes principal amount
• r denotes rate of interest
• n denotes time in years

Here ,

Principal Amount , P = RS. 10,000

Amount , A = RS. 14,641

Time , n = 4 years

Rate of Interest , r = ?

$\implies \bf{14,641=10,000*(1+\dfrac{r}{100}})^4}\\\\\implies \bf{\dfrac{14641}{10000}=(1+\dfrac{r}{100})^4}\\\\\implies \bf{1+\dfrac{r}{100}=\sqrt[4]{\dfrac{14641}{10000}} }\\\\\implies \bf{1+\dfrac{r}{100}=\dfrac{11}{10}}\\\\\implies \bf{\dfrac{r}{100}=\dfrac{1}{10}}\\\\\implies \bf{r=10\;\%}$

Hence the rate of interest per annum is 10 %