Question

Cynthia invests some money in a bank which pays

5% compound interest per year.
She wants it to be worth over £8000 at the end of 3
years.
What is the smallest amount, to the nearest pound, she can invest?

Answer 1

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

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