Mr. Kurris is 50 years old. In four years, his house will be paid off and his daughter will be finished with collage. He wants to take out a five-year level-term life insurance policy with a face value of $750,000. The monthly premium is $61.

Complete question is;

Mr. Kurris is 50 years old. In 4 years, his house will be paid off and his daughter will be finished with college. He wants to take out a 5-year level-term life insurance policy with a face value $750,000. The monthly premium is $61,

a. What will be his total cost for this policy over the 5-year period?

b. If he dies after paying for the policy for 16 months, how much will the insurance company pay his beneficiaries?

c. If he does not die during the 5 years, how much does the insurance company make on this policy?

d. If he dies after paying for the policy for 13 months, how much will the insurance company lose on this policy?

A) $3660

B) $750000

C) $3660

D) $749,207

Step-by-step explanation:

A) Since he wants to take out a five-year level-term life insurance policy, then number of payments for 5 years is;

12 months × 5 = 60 payments.

Since monthly premium is $61, then total cost = 61 × 60 = $3660

B) This is a level-term life insurance policy and so he will be paid the same amount over the entire period of the insurance policy.

Thus If he dies after paying for the policy for 16 months, his beneficiaries will still be paid same $750000

C) if he does not die during the 5 years, the amount the insurance company will make is same as the amount he is due for his premium which is $3660.

D) If he dies after paying for the policy for 13 months, amount that the insurance company will lose is;

>> 750000 - 13(61) = $749,207

The x-intercepts of a graph are found by factoring.  Set y = 0 because the x-intercepts exist when y = 0.  Put this into the quadratic formula to factor.  Like this:   which simplifies to .  The square root of 64 is 8, so the values we find for x are -1 or 3/5.  Because this is a positive parabola, it opens upwards, like a cup, and a cup has a bottom.  So the vertex is a minimum value.  If it was a negative parabola it would open downwards like a mountain and mountains have top.  The coordinates of the vertex can be found by completing the square.  We also could have factored it by completing the square as well!  Should have read that first...but here's how we do that... Move the constant over to the other side of the equals sign.  The rule for completing the square is that the leading coefficient has to be a 1 and it's a 5.  So we will factor out the 5:  .  Take half the linear term, square it and add it to both sides.  Out linear term is 2/5.  Half of 2/5 is 2/10 or 1/5.  1/5 squared is 1/25.  We will add it into the parenthesis, but don't forget about that 5 hanging out front there, refusing to be ignored.  It is a multiplier, so we multiply 5 by 1/25 and add that to the right.  Like this: .  Doing the math on the right and then rewriting the left using the perfect square binomial we created for the purpose of finding the vertex we have  .  Move the constant back over by subtraction to get .  The vertex is .  Graph it by plotting the x-intercepts and the vertex and the y-intercept.  Find other points and graph them if needed.