The difference between compound interest and simple interest on ₹ x at 8% per annum for 2 years is ₹ 48. What is the value of x?

Given that,

Principle amount =Rs. x

Rate of interest $$=8\%$$

time =2 years

Difference between the compound interest and simple interest = Rs. 48

We know that Compound interest=A-P, where A is the total amount and P is the principle amount

$$A=p(1+\dfrac{R}{100})^n$$

Now, substituting the values, $$A=x(1+\dfrac{8}{100})^2 =x(1.08)^2 =1.1664x$$

So, Compound Interest$$ =1.1664x-x =0.1664x--------------(i)$$

Now, for the simple interest,

$$\Rightarrow SI=\dfrac{P\times R\times t}{100}$$

Now, substituting the values,

$$\Rightarrow SI=\dfrac{x\times8\times2}{100}=0.1600x-----------------------(ii)$$

Hence from the equation (i) and (ii)

the required difference $$CI- SI=48$$

$$\Rightarrow 0.1664x-0.1600x=48$$

$$\Rightarrow 0.0064x=48$$

$$\Rightarrow x=\dfrac{48}{0.0064}=7500Rs.$$