Cynthia invests some money in a bank which
5% compound interest per year.
pays
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?
I

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

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.