Answer:
The smallest amount is £6911
Step-by-step explanation:
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
