Question

On what sum will the difference between compound interest and the simple interest for 2 years at ${\displaystyle 7\frac{1}{2}}$ %  be Rs 22.50 ? 

Answer 1

P = x ;  t = 2 years ; r = ${\displaystyle 7\frac{1}{2}}$ % = ${\displaystyle \frac{15}{2}}$ %

For S.I. :

I = ${\displaystyle \frac{\text{P}\times \text{r}\times \text{t}}{100}}$

${\displaystyle =\frac{\text{x}\times \frac{15}{2}\times 2}{100}}$

${\displaystyle =\frac{3\text{x}}{20}}$

For C.I. :

C.I. = ${\displaystyle \text{P}{(1+\frac{\text{r}}{100})}^{\text{t}}-\text{P}}$

${\displaystyle =\text{x}{(1+\frac{\frac{15}{2}}{100})}^2-\text{x}}$

${\displaystyle =\text{x}{(1+\frac{15}{2\times 100})}^2-\text{x}}$

${\displaystyle =\text{x}{(1+\frac{3}{40})}^2-\text{x}}$

= (x × 1.075 × 1.075) -x

= 1.15562S x - x

= 0.155625 x

Given C.I. - S.I. = Rs 22.50 

⇒ 0.155625 x - ${\displaystyle \frac{3\text{x}}{20}=\text{Rs} 22.50}$

⇒  0.155625 x - 0.15 x = Rs 22.50 

⇒  0.005625 x = Rs 22.50 

⇒ x -Rs 4,000 

Hence, sum = Rs 4,000