Rs. 800 at 5% per annum compound interest amounts to 882 in:

The correct answer is Option (4) → 2 years

At compound interest the amount after n years is \(P\left(1+\frac{r}{100}\right)^n\): each year the money is multiplied by the same factor, here 1.05. The number of years is the power of 1.05 that turns 800 into 882.

• Amount after n years: \(800\times(1.05)^n=882\)

• \(\displaystyle (1.05)^n=\frac{882}{800}=1.1025\)

• \((1.05)^2=1.1025\), so \(n=2\) years