Answer :
Answer:
To find the smallest amount Cynthia can invest to have over £8000 at the end of 3 years with a 5% compound interest rate per year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (the initial investment)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
Let's plug in the given values:
A = £8000
r = 5% = 0.05
n = 1 (compounded annually)
t = 3 years
Now we can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
P = £8000 / (1 + 0.05/1)^(1*3)
P = £8000 / (1 + 0.05)^3
P ≈ £6574.10 (rounded to two decimal places)
Therefore, the smallest amount Cynthia can invest, to the nearest pound, is £6,574.