Final answer:
Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this question, the value of x is approximately 0.1, representing an annual interest rate of 10%.
Step-by-step explanation:
Compound interest is calculated using the formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this question, Alex invests £4000 for 7 years, and we need to find the value of x in the compound interest formula. Let's assume x is the annual interest rate. Using the given formula and substituting the values, we have 4000(1 + x/n)^(nt) = 4000(1 + x/1)^(1*7). Simplifying this equation, we get (1 + x)^7 = 2.
To solve for x, we can use trial and error or use a calculator with an exponential function. By trial and error, we find that x ≈ 0.1. Therefore, the value of x is approximately 0.1, representing an annual interest rate of 10%.