Question

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9. (10 marks) Jane Smith wants to retire 20 years from now. Money can be deposited in an account at an actual interest rate of 12% compounded monthly. The future general inflation rate is estimated to be 4% per year. What monthly deposits in actual dollars must be made by the woman until she retires so that she can withdraw an annual amount of $40,000 (in terms of real dollars) over the 15 years following her retirement? Assume that the first withdrawal is made on the date of the last deposit. Also, determine what is the amount of the first withdrawal in terms of actual dollars?

Answer 1

Answer: Months of Deposit 20 12 240 months After 20 Years, Real Dollars of $40,000 means (1.04)20 * 40,000 $87,644.93 in actual dollars at the end of 20 years. And for the next 15 years the real dollar of 40,000 translates to actual dollars, Year Real Actual PV Factor PV Flows 1 87,644.93 91,151 0.8928571 81,384.57 94,797 0.7971939 75,571.39 98,589 0.7117802 70,173.43 24 40,0001,02,532 0.6355181 65,161.05 1,06,633 0.5674269 60,506.69 26 40,0001,10,899 0.506631156,184.78 27 40,0001,15,335 0.452349252,171.58 28 40,0001,19,948 0.4038832 48,445.04 1,24,746 0.36061 44,984.68 0 40,0001,29,736 0.3219732 41,771.49 1 40,0001,34,925 0.287476138,787.81 32 40,0001,40,322 0.256675136,017.25 1,45,935 0.2291742 33,444.59 34 40,0001,51,773 0.2046198 31,055.69 8,23,304.96 87,645 20 40,000 21 40,000 2 40,000 23 40,000 25 40,0001 29 40,000 40,000 |

And the present value of that after 20 years is $823,304.96 And the Monthly Payment for that in actual dollars is RM11.1%.240 periods, 823,304.96) is $832.25 The Amortisation will look like this Year nin Withdrawl in Actual Dollars Interest Closin 20 8,23,305 217,35,660 22 7,32,789 23 7,25,927 24 7,14,449 25 6,97,651 26 6,74,735 6,44,805 28 6,06,847 295,59,720 30 5,02,141 314,32,662 323,49,656 33 2,51,292 135,512 7,35,660 91,15188,279 7,32,789 94,797 8757.25,927 7,14,449 1,02,532 85,734 6,97,651 633 83,718 6,74,735 6,44,805 6,06,847 1,19,948 72,8225,59,720 1,24,746 67,166 5,02,141 1,29,736 60,257 4,32,662 3,49,656 1,40,322 41,959 2,51,292 1.35,512 0 87,645 98,58987,111 1,06,633 1,10,899 1,15,335 77,377 80,968 1,34,92551,919 1,45,93530,155 1,51,77316,261