Find the compound interest on a sum of Rs. 50,000 at the rate of 6% per annum to be compounded half yearly at the end of 2 years. (Approximate to the nearest integer.)

Correct option is C

Given:
Principal (P) = ₹50,000
Rate of Interest (R) = 6% per annum
Time (T) = 2 years
Compounded half-yearly → 2 times in a year
Formula Used:
​$$A = P \times \left(1 + \dfrac{R}{100n}\right)^{nT}$$​​
Compound Interest (C.I.) = A - P
where n = number of times compounded in a year
Solution:
​$$A = 50000 \times \left(1 + \dfrac{6}{100 \times 2}\right)^{2 \times 2} \\[8pt]A = 50000 \times \left(1 + \dfrac{6}{200}\right)^4 \\[8pt]A = 50000 \times (1 + 0.03)^4 \\[8pt]A = 50000 \times (1.03)^4 \\[8pt]A = 50000 \times 1.1255 \approx 56275$$​​
C.I. = A - P = 56275 - 50000 = 6275
Alternate Solution:
Half-yearly rate = 3%
Time = 4 half-years
Effective rate = $$\left(1 + \dfrac{3}{100}\right)^4 - 1 = (1.03)^4 - 1 = 1.1255 - 1 = 0.1255 = 12.55\%$$​​
Compound Interest = 50000 × 12.55% = 50000 × 0.1255 = 6275