At what rate per annum will ₹ 33,000 yield a compound interest of ₹ 31,680 in 2 years interest being compounded yearly?

Correct option is B

Given:
Principal (P) = ₹ 33,000
Time (n) = 2 years
Compound Interest (CI) = ₹ 31,680
Amount (A) = P + CI = 33,000 + 31,680 = ₹ 64,680
Formula Used:
​$$\text{Amount} = \text{Principal} (1 + \frac{Rate}{100})^{time}$$​​
Solution:
​$$64680 = 33000 \left(1 + \frac{R}{100}\right)^2 \\\frac{64680}{33000} = \left(1 + \frac{R}{100}\right)^2 \\1.96 = \left(1 + \frac{R}{100}\right)^2 \\\sqrt{1.96} = 1 + \frac{R}{100} \\1.4 = 1 + \frac{R}{100} \\\frac{R}{100} = 0.4 \\R = 40\%$$


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