If the difference between compound and simple interest on a certain sum of money for 3 years at 2% per annum is ₹604, then what is the sum ?

Difference between $$CI$$ and $$SI$$ ($$D$$) = ₹604

Time ($$n$$) = 3 years

Rate of interest ($$r$$) = 2% per annum

$$SI = \dfrac{P \times r \times n}{100}$$

For $$n = 3$$ and $$r = 2$$:

$$SI = \dfrac{P \times 2 \times 3}{100} = \dfrac{6P}{100} = 0.06P$$

Now, $$CI = P \left[ \left(1 + \dfrac{r}{100}\right)^n - 1 \right]$$

For $$n = 3$$ and $$r = 2$$:

$$CI = P \left[ \left(1 + \dfrac{2}{100}\right)^3 - 1 \right]$$

$$CI = P \left[ (1.02)^3 - 1 \right]$$

$$CI = P [1.061208 - 1]$$

$$CI = 0.061208P$$

The difference $$D = CI - SI$$: $$604 = 0.061208P - 0.06P$$

$$604 = 0.001208P$$

$$P = 5,00,000$$