Final answer:
The future value of £1000 invested at 21% per annum for 2 years is approximately £1464.10. The compound interest earned on the investment is approximately £464.10.
Step-by-step explanation:
The formula for calculating the future value (FV) of an investment with compound interest is: FV = P(1+r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is invested for. In this case, the principal amount is £1000, the annual interest rate is 21%, and the investment is for 2 years. Assuming the interest is compounded annually, the formula becomes:
FV = £1000(1 + 0.21/1)^(1*2)
FV = £1000(1 + 0.21)^(2)
FV = £1000(1.21)^2
FV ≈ £1000(1.4641)
FV ≈ £1464.10
To calculate the compound interest, subtract the principal amount from the future value:
Compound interest = FV - P
Compound interest = £1464.10 - £1000
Compound interest ≈ £464.10