At what rate of interest ₹1,200 becomes ₹1,323 in 2 years where interest gets compounded annually?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5%
Under compound interest, each year’s interest is added to the principal, so the amount after \(n\) years is \(\displaystyle A=P\left(1+\frac{R}{100}\right)^n\).
The amount after 2 years is ₹1,323: \(\displaystyle1200\left(1+\frac{R}{100}\right)^2=1323\)
The money grows by the factor \(\displaystyle\left(1+\frac{R}{100}\right)^2=\frac{1323}{1200}=\frac{441}{400}\) in two years
Its square root is the growth factor for one year: \(\displaystyle1+\frac{R}{100}=\frac{21}{20}\)
\(\displaystyle\frac{R}{100}=\frac{1}{20}\), so \(R=5\%\)