When difference between compound and simple interest for three years is Rs. 122 at 5% interest per annum, the principal is Rs. ______

Correct option is A

Given:

Difference between Compound Interest (CI) and Simple Interest (SI) for 3 years = Rs. 122

Rate (R) = 5% per annum

Time (T) = 3 years

Formula Used: 

CI - SI (for 3 year) = $$\frac{P \times R^2 \times (300 + R)}{100^3}$$​​

Where:

P = Principal, R = Rate %, Time = 3 years

Solution:

Substitute values:

​$$122 = \frac{P \times 5^2 \times (300 + 5)}{100^3} \\ \ \\122= \frac{P \times 25 \times 305}{1000000} \\ \ \\122 = \frac{P \times 7625}{1000000} \\ \ \\P = \frac{122 \times 1000000}{7625} \\ \ \\P = \frac{122000000}{7625} = 16000$$​​

Thus, Principle is Rs. 16,000