£X was invested for 5 years, earning compound interest of 2% per year. After 5 years the total value of the investment was £11,040.81. How do I calculate the value of the invested amount £X?

We know that to calculate the final value V of an investment of £X after t years, earning an interest rate of r being compounded annually, we use the following Compound Interest formula: V = X * (1 + r)^t, where r represents the interest rate as a decimal (e.g. 5% = 0.05). This is because to calculate the value of X after 1 year, we use V = X * (1 + r). Then the formula to calculate the value after 2 years is V = (X * (1 + r)) * (1 + r) = X * (1 + r)² , and then for 3 years it’s V = ((X * (1 + r)) * (1 + r)) * (1 + r) = X * (1 + r)³, and so on. Hence, in our case we use V = X * (1 + r)^t, as we are compounding it for t years.By rearranging the formula, we can calculate the value of £X. We use X = V / (1 + r)^t. Plugging in the known values of V, r and t, we get X = 11040.81 / (1.02)⁵ = £10,000.00 ( to 2 decimal places).