At what rate of interest per annum will Rs. 3000 amount to Rs. 3630 in 2 years, if the interest is compounded annually? Options 5% 12% 11% 10%

To solve this problem, we need to use the formula for compound interest which is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given in the problem: A = Rs. 3630 P = Rs. 3000 n = 1 (since the interest is compounded annually) t = 2 years

We need to find r.

Substituting the given values into the formula, we get:

3630 = 3000 (1 + r/1)^(1*2)

Solving the equation for r:

(3630/3000) = (1 + r)^2

1.21 = (1 + r)^2

Taking the square root of both sides:

1.1 = 1 + r

Subtracting 1 from both sides:

r = 0.1

Converting r to a percentage gives us the annual interest rate:

r = 0.1 * 100 = 10%

So, the annual interest rate is 10%.