Final answer:
To calculate the future value of a £3100 investment at 2.8% compound interest over 8 years, use the formula A = P(1 + r/n)^(nt). Substituting the values, the investment will be worth approximately £3871.51 after 8 years, rounded to the nearest penny.
Step-by-step explanation:
The question asks how much an investment of £3100 at 2.8% compound interest per annum will be worth after 8 years. To calculate this, we use the compound interest formula, which is:
A = P (1 + r/n)^(nt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (£3100 in this case).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Since interest is compounded annually (n=1), and we are given r as a percentage (2.8%), we convert it to a decimal by dividing by 100.
r = 2.8/100 = 0.028
Now, we can put the values into the formula:
A = 3100(1 + 0.028/1)^(1*8)
A = 3100(1 + 0.028)^8
A = 3100(1.028)^8
Using a calculator, we can now compute the value of A after 8 years:
A ≈ £3100 * 1.249003837
A ≈ £3871.51
Thus, the investment will be worth approximately £3871.51 after 8 years, rounded to the nearest penny.