The Johnsons Change Their Life Insurance Coverage Harry and Belinda Johnson spend $20 per month on life insurance in the form of a premium on a $10,000, paid-at-65 cash-value policy on Harry that his parents bought for him years ago. Belinda has a group term i-surance policy from her employer with a face amount of $200,000. By choosing a group life insurance plan from his menu of employee benefits, Harry now has $100,000 of group term life insurance. Harry and Belinda have decided that, because they have no children, they could reduce their life insurance needs by protecting one another's income for only four years, assuming the survivor would be able to fend for himself or herself after that time. They also realize that their savings fund is so low that it would have no bearing on their life insurance needs. Harry and Belinda are basing their calculations on a projected 4 percent rate of return after taxes and inflation. They also estimate the following expenses: $15,000 for final expenses, $20,000 for readjustment expenses,

and $5,000 for repayment of short-term debts.

Requirement:

(a) Should the $3,000 interest earnings from Harry's trust fund be included in his annual income for the purposes of calculating the likely dollar loss if he were to die? (See the discussions about the Johnsons in Chapter 1 beginning on page 34.) Explain your response.

(b) Based on your response to the previous question, how much more life insurance does Harry need? Use the Run the Numbers worksheet on page 366 to arrive at your answer.

(c) Repeat the calculations to arrive at the additional life insurance needed on Belinda's life.

(d) How might the Johnsons most economically meet any additional life insurance needs you have determined they may have?

e) In addition to their life insurance planning, how might the Johnsons begin to prepare for their retirement years?

[1] A Gaussian cube of edge length 1.0 m is located in the xyz space, as shown in the following figure. If the electric field in this space is expressed as: E = 4x ax + 3(yz + 3)ay V/m Determine: a) The electric flux through the top face of the Gaussian cube b) The net charge enclosed by the Gaussian cube Gaussian surface 1- 20m x- 30 mAs discussed in the lecture, the complex envelope of Gaussian beam as a solution to the paraxial Helmholtz Equation is A(r) = q(z) exp - j 29(2)] q(2) = z + jzo- Then, the Gaussian wavefunction is U(r) = A(r) exp(-jkz) 1 A As we write q(z) R(z) TW2(2) Show Gaussian beam can be described as below: Wo U(r) = Ao exp -jkz - jk p2 W (2) exp Wz (2) 2 R(2) + is(=)Question 1. Find the solution to the following system of equations r + 2y + 2 = 1 3r + 7y + 32 =1 -2c - 31 -42 =1 using (a) (2 points) Naive Gaussian elimination, (b) (3 points) Gaussian elimination with partial pivoting, (c) (4 points) Gaussian elimination with complete pivoting, and (d) (4 points) Gaussian elimination with scaled partial pivoting. Make sure to clearly show all your steps, including any row/column exchanges and index/scaling vectors