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Unformatted text preview: Assignment 1: Solutions Econ 181 Wadia Haddaji February 13, 2008 Question 1: You just finished your MBA from a topranked institution and you just got recruited by GoldinSacks, Inc. The job starts immediately and you will be paid monthly, with a starting salary of $7 , 000 per month after tax. You expect your salary to increase at the rate of 4% p.a. (per annum), throughout your career, and you plan to retire in 30 years. Specifically, in your first year of employment you will receive 12 monthly payments of $7 , 000. In your second year, you will receive 12 monthly payments of $7 , 280($7 , 000 x 1 . 04), and soon. The appropriate discount rate is 12% p.a. compound ing monthly. (a) Calculate the future value of your first years salary as of one year from today. (b) Calculate the present value of your total projected future income. [Hint: Think of your annual salary as a 30 year growing annuity, where the first annuity payment is the value that you calculated in part (a). Bear in mind that you will need to convert the 12% monthly compounding rate into an effective annual rate since the growth rate of the salary is quoted on an annual basis. Also, the formula for a growing perpetuity with a growth rate of g is A t,g = a t +1 / ( i g )]. (a) Calculate the future value of your first years salary as of one year from today. The relevant parameters are as follows: Monthly Salary = $7 , 000 m=12 R=12% i=1% g annual = 4% g monthly =0.3% First convert monthly salary to yearly by recognizing you need to find the future value of a 12period annuity: $7000 * [(1 . 01 12 1) / . 01] = $88 , 777 . 52 1 (b) We need to find the value of a growing perpetuity starting next month. Note that the growth rate of her salary is in annual terms so we need to state the interest rate in this frequency as well: the effective annual interest rate is: (1 + 0 . 01) 12 1 = 0 . 126825 or 12 . 68%....
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 Spring '07
 HADDAJI

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