Answer: The value of x is 3.45%
Explanation:
We can solve the problem by using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time in years
In the first year, Charlie gets 2% interest, compounded annually. So, using the formula, we have:
A1 = 4000(1 + 0.02/1)^(1*1)
A1 = 4080
After the first year, Charlie has £4080 in her account. For the next two years, she gets x% interest, compounded annually. Using the formula again, we have:
A2 = 4080(1 + x/100/1)^(1*2)
A2 = 4080(1 + x/100)^2
Finally, after three years, Charlie has £4228.20 in her account. So, we can set up an equation:
A1 * A2 = 4000 * (1 + 0.02) * 4228.20
Substituting the values of A1 and A2, we get:
4080(1 + x/100)^2 = 4366.4496
Dividing both sides by 4080, we get:
(1 + x/100)^2 = 1.0694
Taking the square root of both sides, we get:
1 + x/100 = 1.0345
Subtracting 1 from both sides and multiplying by 100, we get:
x = 3.45
Therefore, the value of x is 3.45%.