Cynthia invests some money into a bank which pays 5% compound interest per year she wants it to be worth over £8000 at the end of three years what is the smallest amount to the nearest pound she can invest

£6911 is the smallest amount Cynthia should invest to get £8000 after three years

Step-by-step explanation:

lets Assume that amount needs to invested for three years = £ x

Rate of Interest = R = 5% per year

Duration in years = n = 3 year

Amount expected after three years when compounded annually =  A = £8000

Formula for Amount of compound interest annually is a follows

A = P( 1 + R/100)^n

In our case Principal P = x , Amount A = 8000 , R = 5% and n = 3( since compounded annually). On substituting these values in above formula we get

8000 = x ( 1 + 5/100)^3

⇒8000 = x ( 105/100)^3

⇒8000 = x ( 21/20 )^3

⇒(8000 × 20 × 20 × 20)/(21×21×21) = x

⇒x = 6910.70≈6911

Hence £6911 is the smallest amount Cynthia should invest to get £8000 after three years