At what rate per cent will a sum of ` 2000 amount to ` 2880 in 2 years if the interest iscompounded annually?

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 = the 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 = 2880 P = 2000 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:

2880 = 2000 (1 + r/1)^(1*2)

Solving this equation for r gives us the annual interest rate.

1. Divide both sides of the equation by 2000:

2880/2000 = (1 + r)^2

1.44 = (1 + r)^2

2. Take the square root of both sides:

sqrt(1.44) = 1 + r

1.2 = 1 + r

3. Subtract 1 from both sides to solve for r:

r = 1.2 - 1

r = 0.2

So, the annual interest rate is 0.2, or 20% when expressed as a percentage.