The difference between Compound Interest and Simple Interest on a certain sum for 2 years at 12.5% rate is Rs.45. What is the sum?

Given,

The difference between Compound Interest and Simple Interest on a certain sum for 2 years at 12.5% rate is Rs.45.

Formula for 2 years difference is,

$$\frac{{P}{R^2}}{100^2}$$

therefore, from the question, we know that $$\frac{{P}{R^2}}{100^2}$$ = 45

substituting R in the formula, $$\frac{{P}\times{(12.5)^2}}{100^2}$$ = 45

∴ $${P}$$ = $$\frac{{45}\times{100^2}}{12.5^2}$$

   $${P}$$ = $$\frac{{45}\times{1000}\times{1000}}{{125}\times{125}}$$

   $${P}$$ = 2880  

∴ The sum is 2880.