On compound interest, ₹2,000 amounts to ₹2,226.05 in 2 years. What is…

The correct answer is Option (2) → 5.5%

With compound interest compounded yearly, the amount after \(n\) years is \(\displaystyle A=P\left(1+\frac{r}{100}\right)^{n}\): each year the money is multiplied by the same factor \(1+\frac{r}{100}\).

• In 2 years the money is multiplied by the factor twice: \(\displaystyle\left(1+\frac{r}{100}\right)^{2}=\frac{2226.05}{2000}=1.113025\)

• The yearly factor is its square root: \(\displaystyle 1+\frac{r}{100}=\sqrt{1.113025}=1.055\)

• \(r=5.5\%\)

Shortcut: Test the options by the yearly factor.

• At 5.5% the factor is 1.055, and \(1.055^{2}=1.113025\)

• \(2000\times1.113025=2226.05\), the amount given, so 5.5% fits