Cynthia invests some money in a bank which pays 5% compound interest per year. she wants it to be worth over £8000 after 3 years. what is the smallest amount, to the nearest pound, she can invest? simple steps ?

To get the smallest amount one can invest in 3 years at a rate of 5% to obtain £8000 we use the compound formula given by:
A=p(1+r/100)^n
where:
A=future amount
p=principle
r=rate
n=time
From the question:
A=£8000, r=5%, n=3
thus plugging the values in the formula and solving for p we get:
8000=p(1+5/100)6n
8000=1.157625p
thus
p=6910.700
Hence the smallest amount is £6910.70~£6910

4would have to be the correct answer