A sum of ₹8,000 is invested at an annual interest rate of 12% compounded half-yearly for 2 years. Calculate the compound interest earned at the end of 2 years.(Rounded off to the nearest integer)

Correct option is B

Given:

Principal (P) = ₹8,000
Rate (R) = 12% per annum
Time (T) = 2 years
Compounding frequency = Half-yearly (2 times a year)

Formula Used:
Compound Interest (CI) = $$P \left(1 + \frac{R}{n}\right)^{nt} - P$$​​
Where:
P = Principal
R = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time the money is invested for, in years

Solution:
Here, P = 8,000, R = 12% = 0.12 , t = 2 years, and n = 2 (because interest is compounded half-yearly).

Substitute these values into the compound interest formula:

CI = 80$$00 \left(1 + \frac{0.12}{2}\right)^{2 \times 2} - 8000$$​

CI = 80$$00 \left(1 + 0.06\right)^4 - 8000$$​

CI = 80$$00 \left(1.06\right)^4 - 8000$$​

CI $$= 8000 \times 1.262476 - 8000$$​

CI = 10100 - 8000

CI = 2100