₹ 2000 amounts to ₹ 2226.05 in 2 years on compound interest. What is the rate of interest per annum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5.5%
Under compound interest, the amount after \(n\) years is \(A=P\left(1+\frac{R}{100}\right)^n\): each year’s interest is added to the principal and earns interest itself.
\(\displaystyle 2000\left(1+\frac{R}{100}\right)^2=2226.05\)
\(\displaystyle \left(1+\frac{R}{100}\right)^2=\frac{2226.05}{2000}=1.113025\)
\(\displaystyle 1+\frac{R}{100}=1.055\), since \(1.055^2=1.113025\)
\(R=5.5\%\)