Providesolutionsforthefollowingproblems. Questions.
For an actuarial present value denoted by Jim, describe the benefit. Show that -;i = 151x AXE 'l" D". For independent lifetimes T(I] and y), show that Cov(vTix3], vim\") = (A: flxyfly - Aw), Express, in terms of single- and joint-life annuity values, the actuarial present value of an annuity payable continuously at a rate of 1 per year while at least one of (25) and (30} survives and is below age 50. Express, in terms of single and joint-life annuity values, the actuarial present value of a deferred annuity of 1 payable at the end of any year as long as either (25) or (30} is living after age 50. Express, in terms of single- and joint-life annuity values, the actuarial present value of an n-year temporary annuity-due, payable in respect to (Jry), provid- ing annual payments of 1 while both lives survive, reducing to 1/ 2 on the death of (x) and to 1/3 on the death of {3;}. An annuitywimmediate of 1 is payable to (x) as long as he lives jointly with (y) and for a years after the death of (y), except that in no event will payments be made after m years from the present time, at > :1. Show that the actuarial present value is \"xl + EX Igathqycml' Obtain an expression for the actuarial present value of a continuous annuity of 1 per annum payable while at least one of two lives (40) and [55] is living and is over age 60, but not if (40) is alive and under age 55. A joint-and-survivor annuity to (x) and (y) is payable at an initial rate per year while (3:) lives, and, if (y) survives (x), is continued at the fraction p, U2 1: p E 1, of the initial rate per year during the lifetime of (y) following the death of (x). a. Express the actuarial present value of such an annuitydue with an initial rate of 1 per year, payable in m-thly installments, in terms of the actuarial present values of single-life and joint-life annuities. b. A joint-and-survivor annuity to (x) and {y} and a life annuity to (x) are said to be actuarially equivalent on the basis of stated assumptions if they have equal actuarial present values on such basis. Derive an expression for the ratio of the initial payment of the joint-and-survivor annuity to the payment rate of the actuarially equivalent life annuity to (x). . Show that a. g, = fix; 853'), [This exercise depends on material in Section 9.9.] a __ _ _ b. E a\" = mix) a\4 Present Value (LO9-4) you will receive $6,800 three years from now. The discount rate is 10 percent. $6,800 a . What is the value of your investment two years from now? Multiply $6,800 by 1 or divide by 1.10 (one year's discount rate at 10 percent). b . 1.10 What is the value of your investment one year from now? Multiply your answer to part a by 1 C . 1.10 What is the value of your investment today? Multiply the part b answer by 1 d . 1.10 Use the formula to find the present value of $6,800 received three years from now at 10 percent interest. Use > PV = FV x- And Time Value Tables Remember to show all work. a b C d3. Assuming following equations for a closed economy, please answer the questions below. Consumption = C = co + CYD Taxes=T = to + t,Y Investment = I = bo + b,Y - bzi Goverment Expenditures=G a. Which terms are considered constant/exogenous and endogenous in this economy? Please explain your answers intuitively. b. Please explain consumption, Tax and investment functions for this economy in detail. c. Please write the demand function for this economy and please explain it. d. Making relevant assumptions please solve the system for the equilibrium level of income e. Please derive the autonomous consumption multiplier. f. Utilizing graphs please derive and explain the IS curve for this economy. You are expected to drive it from the Keynesian cross. Make sure that you are labeling all the axes properly. g. Please derive an equation for the IS curve mathematically. h. Assuming that the central bank of the country announces interest rate targets, show equilibrium condition graphically with the help of the IS and LM framework. i. What happens to main macroeconomic variables (C, I, i, Y. T and Private Saving. Total Saving) if expected profits of investors decline and consumers become much more pessimistic about the future of the economy? Please utilize the IS and LM framework. Graphical description and intuitive explanations are enough. j. What happens to main macroeconomic variables (C, I, i, Y, T) if the central bank responds to an inflationary pressure in this economy while the goverment increases its expenditures (In the previous version it was read as "the government decreases Taxes': this will not cause a significant change in the answer) to be able to have an advantage in an upcoming election. Graphical description and intuitive explanations are enough.You will receive $9,800 three years from now. The discount rate is 10 percent. a. What is the value of your investment two years from now? Multiply $9,800 * (1/1.10) or divide by 110 (one year's discount rate at 10 percent). (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of investment b. What is the value of your investment one year from now? Multiply your answer to part a by (1/1.10). (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of investment c. What is the value of your investment today? Multiply your answer to part b by (1/1.10). (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of investment d. Use the formula Pv = FV * (1/ (1+1) ?) to find the present value of $9,600 received three years from now at 10 percent interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value
