Final answer:
For Sam's investment of £5000 at 2.8% per annum compound interest for 4 years, the value at the end of 4 years is approximately £5483.86. For Andy's investment of £12,000 in a variable rate compound interest account with interest rates of 2%, 3.5%, and 5% for the first, second, and third years respectively, the value at the end of 3 years is approximately £13,311.27.
Step-by-step explanation:
For Sam's investment, we can use the compound interest formula: A = P(1 + r/n)^(nt)
Here, P = £5000 is the principal amount, r = 2.8% per annum, n = 1 (since it is compounded annually), and t = 4 years.
So, A = £5000(1 + 0.028/1)^(1*4) = £5000(1.028)^4 ≈ £5483.86
For Andy's investment, we can calculate the value at the end of each year and compound the amount for the next year.
During the first year, the amount becomes £12,000(1 + 0.02) = £12,240.
During the second year, it becomes £12,240(1 + 0.035) = £12,677.40.
During the third year, it becomes £12,677.40(1 + 0.05) = £13,311.27.
So, at the end of 3 years, Andy's investment will be approximately £13,311.27.