The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:​

Correct option is B

Given:

Principal P = ₹17700

Rate r = 4% p.a.

Time t = 2 years (compounded annually)

Find: CI - SI

Formula Used:

​$$\text{SI} = \dfrac{P r t}{100}$$​​

​$$\text{CI} = P\left(1+\dfrac{r}{100}\right)^{t} - P$$​​

For 2 years (annual compounding): $$\text{CI} - \text{SI} = P\left(\dfrac{r}{100}\right)^2$$​​

Solution:
CI - SI = $$17700 \times \left(\frac{4}{100}\right)^2$$​​
= 1770$$0 \times 0.0$$​016
= ₹28.32

Alternate Method:
​$$\text{SI} = 17700 \times \dfrac{4}{100} \times 2 = ₹1416$$​​
​$$\text{CI} = 17700\left[\left(1+\dfrac{4}{100}\right)^2-1\right] = 17700(1.0816-1) = 17700 \times 0.0816 = ₹1444.32$$​​
Difference = 1444.32 - 1416 = ₹28.32.