The amount needed in the account when Frost retires is given by the annuity formula. Compounding is 2 times per year.
.. A = Pi/(n(1 -(1 +r/n)^(-nt)))
.. 17900 = P*.08/(2*(1 -(1 +.08/2)^(-2*12)))
.. 17900 = P*.04/(1 -(1.04^-24))
.. P ≈ 272,920.64
The compound interest formula can be used to find the present value required. 4015 days is 11 years (ignoring leap years), so the amount to deposit can be calculated from
.. A = P*(1 +r/n)^(nt)
.. 272,920.64 = P*(1 +.08/2)^(2*11) = P*1.04^22
.. P ≈ 115,160.33
We don't know about the company's obligation to Robert. To fulfill its obligation to Frost, it must deposit 115,160.33 today.
Right away we know we don't have fractions; the midpoint is the average of the coordinates, so if it and one endpoint are integers so is the other endpoint.
We can do a kind of point arithmetic:
C = (A+B)/2
2C = A+B
B = 2C - A
B = 2(6,1) - (1,3) = (12,2)-(1,3)=(11,-1)
Answer: That's none of the above, but a typo away from the first choice.
It would make you less likely because you might have to pay the money you were gonna pay to the people who did the car loan.
The coordinates for D are (-4, -7)
First we must locate point B as it is vital to finding the midpoint of BD. To do this, we take the average of the endpoints AC since B is its midpoint.
x values = -9 + 1 = -8
Then divide by 2 for the average -8/2 = -4
y values = -4 + 6 = 2
Then divide by 2 for the average 2/2 = 1
Therefore B must be (-4, 1)
Now we know the values of E must be the average of B and D. So we can write equations for each coordinate since we know they are averages.
x - values = (Bx + Dx)/2 = Ex
(-4 + Dx)/2 = -4 ---> multiply both sides by 2
-4 + Dx = -8 ---> add -4 to both sides
Dx = -4
y - values = (By + Dy)/2 = Ey
(1 + Dy)/2 = -3 ---> multiply both sides by 2
1 + Dy = -6 ---> subtract 1 from both side
Dy = -7
So the coordinates for D must be (-4, -7)
