Explanation

Principal amount (P) = Rs. 800

Rate of interest (R) = 5% per annum

Compound interest (CI) = Rs. 882 - Rs. 800 = Rs. 82

Using the compound interest formula:

A = P (1 + R/100)^n

where A is the amount after n years, we can plug in the values:

882 = 800 (1 + 5/100)^n

Simplifying the equation:

(1.05)^n = 882/800

(1.05)^n = 1.1025

Now, taking the logarithm of both sides (base 1.05):

n = log1.05(1.1025)

n ≈ 2

So, it will take approximately 2 years for Rs. 800 to amount to Rs. 882 at 5% p.a. compounded annually.