Question

If the compound interest on a certain sum of money for 2 years is Rs.2,700 and the simple interest on the same sum for the same period is Rs.2,500, the rate of interest will be

• A. 16 percent
• B. 10 percent
• C. 18 percent
• D. 24 percent

Answer 1

The correct option is A 16 percent

Let the sum of money be ${}^{\prime }{x}^{\prime }$.

$T=2$ years

$C.I=2700$. , Rate=R

$A=P{(1+\frac{R}{100})}^2$

$\Rightarrow (x+2700)=x{(1+\frac{R}{100})}^2⟶\left(I\right)$

Now,

$S.I=2500$

$\Rightarrow 2500=\frac{x\times R\times 2}{100}$

$\Rightarrow xR=125000$

$\Rightarrow R=\frac{125000}{x}\to \left(II\right)$

Putting ${}^{\prime }{x}^{\prime }$ in eq (I)

$(\frac{125000}{R}+2700)=\frac{125000}{R}{(1+\frac{R}{100})}^2$

$\Rightarrow \left(\frac{125000+2700R}{R}\right)=\frac{125000}{R}{(1+\frac{R}{100})}^2$

$\Rightarrow (125000+2700R)=125000{(1+\frac{R}{100})}^2$

$\Rightarrow 1250+27R=1250{(1+\frac{R}{100})}^2$

$\Rightarrow 1250+27R=1250(1+2\left(0.0R\right)+{\left(0.0R\right)}^2)$

$\Rightarrow 1250+27R=1250+25R+0.125R^2$

$\Rightarrow 0.125R^2-2R=0$

$\Rightarrow R(0.125R-2)=0$

$\Rightarrow R=0$ or $0.125R-2=0$

But $R$ can't be $0$.

$\therefore 0.125R-2=0$

$\Rightarrow R=\frac{2}{0.125}=16$

$\therefore R=16$%