Question

A certain sum of money at compound intrest becomes7396 in 2 years and 7950.70 in 3 years find the rate of intrest

Answer 1

$\mathfrak{Answer:}$

= 7.5%.

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

Let the principle be Rs. P and rate of interest be r %.

• Amount = Rs.7396.
• Time = 2 years

$\bigstar\quad\textbf{We know that : \boxed{\bold{Amount=P\left(1+\dfrac{r}{100}\right)^n.}}}\\\\\mathfrak{According\;to\;Question}\\\\\\\implies\tt{7396=P\left(1+\dfrac{r}{100}\right)^2.........(1).}\\\\\\\bold{Again:}\\\\\\\bullet\quad\textsf{Amount = Rs. 7950.70.}\\\\\bullet\quad\textsf{Time = 3 years.}\\\\\\\implies\tt{7950.70=P\left(1+\dfrac{r}{100}\right)^3...........(2)}$

$\underline{\bold{Dividing\;eq.(2)\;by\;eq.(1)\;we\;get,}}\\\\\\\implies\tt{\dfrac{P\left(1+\dfrac{r}{100}\right)^3}{P\left(1+\dfrac{r}{100}\right)^2}=\dfrac{7950.70}{7396}}\\\\\\\implies\tt{1+\dfrac{r}{100}=1.075}\\\\\\\implies\tt{\dfrac{100+r}{100}=1.075}\\\\\\\implies\tt{100+r=1.075\times 100}\\\\\\\implies\tt{100+r=107.5}\\\\\\\implies\tt{r=107.5-100}\\\\\\\therefore\quad\tt{r=7.5\%.}\\\\\\\\\boxed{\boxed{\bold{Rate\;of\;the\;Interest=7.5\%.}}}$