Find the compound interest (in Rs.) on Rs. 2,00,000 in 1.5 years at 4% per annum, the interest being compounded half-yearly.

Correct option is B

Given:
Principal (P) = ₹2,00,000
Rate (r) = 4% per annum
Time (t) = 1.5 years
Compounding = Half-yearly
Formula Used:
Compound Interest (CI) = Amount (A) - Principal (P)
Amount (A) = $$P \times \left(1 + \frac{r}{n} \right)^{n \times t}$$​​
Where:
n = Number of times interest is compounded per year
t = Time in years
Solution:
​$$A = ₹2,00,000 \times \left(1 + \frac{4/2}{100} \right)^{2 \times 1.5} \\\Rightarrow A = ₹2,00,000 \times \left(1 + \frac{2}{100} \right)^3 \\\Rightarrow A = ₹2,00,000 \times (1 + 0.02)^3 \\\Rightarrow A = ₹2,00,000 \times 1.023 \\\Rightarrow A = ₹2,00,000 \times 1.061208 \\\Rightarrow A = ₹2,12,241.60$$​​
Compound Interest (CI) = A - P
=> CI = ₹2,12,241.60 - ₹2,00,000
=> CI = ₹12,241.60