Question

At what rate percent will a sum of Rs. 3750 amount to Rs. 4374 in 2 years, If the interest is compounded annually?​

Answer 1

Answer

Given,

A=4374

P=3750

N=2 years

R=?

As we know,

A=P(1+R/100)^2

4374=3750(100+R)^2/10000

4374*1000/375=10000+200R+R^2

11664=10000+200R+R^2

R^2+200R-1664=0

R^2+208R-8R-1664=0

R(R+208)-8(R+208)=0

(R+208)(R-8)=0

Either R+208=0 OR R-8=0

R=-208 OR R=8

Since rate will never be negative so required value of R=8% ANS

Answer 2

AnswEr :

$\bf{Given}\begin{cases}\sf{Principal = Rs. \:3750}\\\sf{Time = 2 \:years}\\ \sf{Amount = Rs. \:4374}\\\sf{Rate = ? \:p.c.p.a} \end{cases}$

$\rule{140}{2}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$\longrightarrow \tt{Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}}\\\\\\\longrightarrow \tt 4374 = 3750 \times \bigg(1 +\dfrac{r}{100}\bigg)^{2}\\\\\\\longrightarrow \tt \cancel\dfrac{4374}{3750} = \bigg(1 +\dfrac{r}{100}\bigg)^{2}\\\\ \qquad \scriptsize{\bf{ \dag} \:\textsf{Dividing LHS by 6}} \\\\\longrightarrow \tt \dfrac{729}{625} = \bigg(1 +\dfrac{r}{100}\bigg)^{2}\\\\\\\longrightarrow \tt \sqrt{\dfrac{729}{625}} = 1 + \dfrac{r}{100}\\\\\\\longrightarrow \tt \sqrt{\dfrac{27 \times 27}{25 \times 25} } = 1 + \dfrac{r}{100}\\\\\\\longrightarrow\tt\dfrac{27}{25} = 1 + \dfrac{r}{100}\\\\\\\longrightarrow\tt\dfrac{27}{25} - 1 = \dfrac{r}{100}\\\\\\\longrightarrow\tt\dfrac{2}{ \cancel{25}} = \dfrac{r}{\cancel{100}}\\\\\\\longrightarrow\tt2 = \dfrac{r}{4}\\\\\\\longrightarrow\tt2 \times 4 = r\\\\\\\longrightarrow \boxed{\red{\tt r = 8\%}}$

⠀

$\underline{\therefore\:\textsf{Sum will compounded at \textbf{8\% p.c.p.a.}}}$