Question

In how many years will rs700 amount to rs847 at a compound interest rate of 10 pcpa​

Answer 1

$\underline{\bold{Given}}$

Principle = Rs.700

Amount = Rs.847

Rate = 10% per annum.

$\underline{\bold{To\:find,}}$

Time = ?

Compounded annually,

We know that,

$\boxed{\bold{Amount = P {( 1 + \dfrac{r}{100} )}^{n}}}$

According to the question,

$\implies\bold{Rs.847=Rs.700{(1+\dfrac{10}{100})}^{n}}$

$\implies\bold{Rs.847=Rs.700{(\dfrac{11}{10})}^{n}}$

$\implies\bold{\dfrac{847}{700}={(\dfrac{11}{10})}^{n}}$

$\implies\bold{\dfrac{121}{100}={(\dfrac{11}{10})}^{n}}$

$\implies\bold{{(\dfrac{11}{10})}^{2}={(\dfrac{11}{10})}^{n}}$

when the fractions on both side is same then the powers are also same....

$\implies\bold{n = 2}$

$\therefore{\bold{Time=2years}}$

Answer 2

$\mathfrak{Answer:}$

= 2 years.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\bold{Given\:in\:the\:Question:}}$

• Principle = P = Rs. 700
• Amount = A = Rs. 847.
• Rate = 10 %.

$\bold{Solution:}$

Let the time be n years.

$\mathfrak{According\:to\:question:}$

$\boxed{\bold{Amount=P\left(1+\dfrac{r}{100}\right)^n}}\\\\\\\implies\tt{847=700\left(1+\dfrac{10}{100}\right)^n}\\\\\\\implies\tt{\dfrac{847}{700}=\left(1+\dfrac{1}{10}\right)^n}\\\\\\\implies\tt{\left(\dfrac{11}{10}\right)^2=\left(\dfrac{11}{10}\right)^n}\\\\\\\implies\tt{n=2}\\\\\\\\\boxed{\boxed{\bold{Time=2\:years.}}}$