b. what must be the face value of the two zeros to fund the plan?

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $ 1 million per annum. The interest rate is 10%. You plan to fully fund the obligation using five-year and 20-year maturity zero-coupon bonds. a. how much market value of each of the zeros will be necessary to fund the plan if you desire an immunised position?

A pension plan is obligated to make disbursements of $1 million, $2 million, $5 million, and $1 million at the end of each of the next four years, respectively. If the plan wants to fully fund and immunise its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? Assume the interest rate is 10% annually. Group of answer choicesDuration is 2.6019Duration is 2.7329Duration is 2.6873Duration is 2.5871

Show that his optimal consumption plan (c0; c1; c2) fromthe perspective of his period 0 self is equal to (1:4; 0:8; 0:8). Givenhe consumes c0 = 1:4 in period 0 (and hence saves 0:6) work out theamounts ^c1 and ^c2 that he will actually choose to consume in periods1 and 2.For the last question, suppose that instead of being able to put money inthe bank to earn interest at the rate of 100% per period, Brian can insteadpurchase a quantity q  0 of an annuity at a per-unit price p. That is, eachunit of the annuity costs him p million dollars in period 0 and pays out 1million dollars in period 1 and 1 million dollars in period 2. For example, ifhe purchases the fraction 0:2 of a unit of the annuity in period 0 at a costof 0:2  p then the annuity will pay him 0:2 (of a million dollars) in period1 and 0:2 in period 2

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $25,000 annually for four years, and the cost of capital is 9%?Question 2Select one:a.$19,007.00b.$25,000.00c.$91,743.12d.$80,993.00

(b) (10 points) Utilizing the fact that his marginal utility of consumptionmu (c) = 2 c, show that in period 0 his optimal consumption plan(measured in millions of dollars) is(c0; c1; c2) = 87 ; 87 ; 87.(c) (5 points) Explain qualitatively how this optimal plan would changeif the interest rate was greater than 1. Explain qualitatively how thisoptimal plan would change if the interest rate was less than 1.(d) (10 points) If Brian chooses to consume c0 = 8=7 in period 0, explainwhat his intertemporal budget set B1 ((c0; c1; c2)) will be in period 1.Show that the continuation of his original consumption plan (c1; c2) =(8=7; 8=7) is indeed the optimal consumption plan for him to choosein period 1 from this budget set. Explain what property of his choicebehavior does this reáect.