1. (50 points) Brian is about to take early retirement at the age of 45.His current wealth is $2 million and he plans to use this wealth to fund hisconsumption over the remaining three periods of his life.1 Any money thathe does not spend on consumption in period 0 can be put in the bank whereit will earn interest at the rate of 100% per period. That is, r = 1, so ifchooses not to consume an amount s of his $2 million in period 0 he willhave s (1 + r) = 2s available at the beginning of period 1. Similarly, anymoney he does not spend on consumption in period 1 can be put in the bankwhere it will also earn interest at the rate of r = 1.(a) (5 points) Explain why his intertemporal budget set B can be de-scribed as follows:B =(c0; c1; c2)  (0; 0; 0) : c0 + 12 c1 + 14 c2  2

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

John is 30 years old. He comes up with a plan to save for his retirement at 65 years. Currently, he has saved $20,000 in a balanced superannuation account earning 5.1% p.a. compounded annually. He has set himself a retirement target of $2,000,000. How much must be deposited every year into John's superannuation account, starting next year, to reach his target? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

You inherit $300,000 from your parents and want to use the money to supplement your retirement. You receive the money on your 65th birthday, the day you retire. You want to withdraw equal amounts at the end of each month for the next 20 years. What constant amount can you withdraw each month and have nothing remaining at the end of 20 years if you are earning 7% interest compounded monthly?

You are saving for retirement. You plan to retire when you reach 65 yearsold. To live comfortably during retirement, you plan to withdraw moneyfrom your savings account $48,000 each year. Suppose today is your 25thbirthday, and you decide, starting today and continuing on every yearup to your 64th birthday, that you will put the same amount into a savingsaccount. If the interest rate is 2.4% per annum, compounded annually,how much must you set aside each year to make sure that you will haveenough money in the account on your 65th birthday in order to be ableto withdraw $48,000 per year when you retire and you expect to live untilyour are 90 years old (i.e., the first withdrawal is on your 65th birthday andthe last withdrawal occurs on your 89th birthday)?

A father left a will of Rs. 85,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attains the age of 18 years. If the money is invested at 10% p.a. simple interest, then find how much (in Rs.) would the son aged 10 years gets at the time of the execution of the will.1)  30,0002)  40,0003)  45,0004)  48,000