The difference between the compound interest, compounded annually and the simple interest if ₹47,100 is deposited at 9% rate of interest per annum for 2 years is:

Correct option is C

Given:

Principal P = ₹47,100

Rate r = 9% p.a.

Time t = 2 years

Interest types: Simple Interest (SI) and Compound Interest (CI, compounded annually)

Formula Used:

​$$\text{SI} = \dfrac{P \times r \times t}{100}$$​​

​$$\text{CI} = P\big[(1+\dfrac{r}{100})^t - 1\big]$$​​

(Shortcut for 2 years) $$\text{CI} - \text{SI} = P \left(\dfrac{r}{100}\right)^2$$​​

Solution:

​$$\text{SI} = \frac{47100 \times 9 \times 2}{100} = 47100 \times 0.18 = ₹8{,}478 \\ \ \\ \ \\\text{CI} = 47100\left[(1.09)^2 - 1\right] = 47100(1.1881 - 1) = 47100 \times 0.1881 = ₹8{,}859.51$$​​

Difference:

CI - SI = 8,859.51 - 8,478 = ₹381.51

Alternate Method:

​$$\text{CI} - \text{SI} = P\left(\frac{r}{100}\right)^2 = 47100 \times (0.09)^2 = 47100 \times 0.0081 = ₹381.51.$$​​