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ADMS3530 Fall 2010 Assignment #1 2 Question 1 (TVM) 20 marks This question consists of three independent parts: a), b) and c) a) Elena plans to retire in 12 years from today and she wants to have an annuity of \$40,000 a year for 25 years after retirement. Elena wants to receive the first annuity payment the same day as her retirement date. How much must Elena invest today (one lump sum) in order to meet her retirement goal if the annual interest rate is 6% compounded annually? (7 marks) b) Elena is wondering how long it will take her to accumulate \$1 million if she begins depositing \$800 in the bank every month starting one month from now. The bank will pay her an EAR of 6% with monthly compounding. Please calculate for her the number of years it will take to reach her \$1million goal. (7 marks) c) If Elena can earn an EAR of 8% (with monthly compounding) on her funds and if she can manage to save \$1000 each month, how many years will it take her to accumulate \$1,000,000 under this new scenario? (6 marks) Solution a) The present value of the 25-year annuity due over Elena’s retirement is: PV ordinary annuity: PVA = PMT [1-(1 + r) -n / r] = 40,000 x {[1-(1.06) -25 ]/ 0.06]} = 40,000 x (12.7834) = \$511,334.25 P V annuity due = 511,334.25 x (1.06) = 542,014.30 This will also be the future value of Elena’s savings account in 12 years from today. Therefore, the principal amount that Elena should deposit into her account today is: PV = FV /(1 + r ) t = 542,014.30 / (1.06) 12 = 269,364.50 b) First, we need to find the corresponding monthly interest rate: r m = (1 + EAR) 1/m -1 = (1.06) 1/12 -1 = 0.004868 The savings account is an annuity for n months where 1,000,000 is the FV FV = PMT x [(1+r m ) n -1] / r m 1,000,000 = 800 x [(1.004868) n -1]/.004868 Solving for n , the number of months, by your financial calculator, you should get:
ADMS3530 Fall 2010 Assignment #1 3 PV = 0; FV = 1,000,000; PMT = -800, I/Y = 0. .4868

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This note was uploaded on 12/15/2011 for the course ADMS 3530 taught by Professor Unknown during the Spring '09 term at York University.

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