Test Version B 53 min Part B: EXTRA CREDIT (5 points) 21) Your sister turned 35

Question

Test Version B 53 min Part B: EXTRA CREDIT (5 points) 21) Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 75% peryear. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year 30 yeas TV n: 30 N 0

Explanation / Answer

Future value of annuty = p[(((1+r)^(n-1))-1)/r]

p = 7500

r = 0.075

n = 30-1 = 29

Future Value = 775495.52

Monthly Withdrawels

Future Value divide by Sum of Present Value of 7.5% for 20 years

Present Value of 7.5% for 20 years = 11.14695

Present value = 69570.22 per installment

Year Installment Interest Balance 36 7500 - 7500 37 7500 562.5 15562.5 38 7500 1167.1875 24229.6875 39 7500 1817.226563 33546.91406 40 7500 2516.018555 43562.93262 41 7500 3267.219946 54330.15256 42 7500 4074.761442 65904.91401 43 7500 4942.86855 78347.78256 44 7500 5876.083692 91723.86625 45 7500 6879.289969 106103.1562 46 7500 7957.736716 121560.8929 47 7500 9117.06697 138177.9599 48 7500 10363.34699 156041.3069 49 7500 11703.09802 175244.4049 50 7500 13143.33037 195887.7353 51 7500 14691.58015 218079.3154 52 7500 16355.94866 241935.2641 53 7500 18145.14481 267580.4089 54 7500 20068.53067 295148.9396 55 7500 22136.17047 324785.11 56 7500 24358.88325 356643.9933 57 7500 26748.2995 390892.2928 58 7500 29316.92196 427709.2147 59 7500 32078.1911 467287.4058 60 7500 35046.55544 509833.9613 61 7500 38237.5471 555571.5084 62 7500 41667.86313 604739.3715 63 7500 45355.45286 657594.8244 64 7500 49319.61183 714414.4362 65 7500 53581.08271 775495.5189 Year Withdrawel Interest Balance 66 69570.22 58162.16392 764087.4628 67 69570.22 57306.55971 751823.8025 68 69570.22 56386.78519 738640.3677 69 69570.22 55398.02758 724468.1753 70 69570.22 54335.11315 709233.0684 71 69570.22 53192.48013 692855.3286 72 69570.22 51964.14964 675249.2582 73 69570.22 50643.69437 656322.7326 74 69570.22 49224.20494 635976.7175 75 69570.22 47698.25381 614104.7513 76 69570.22 46057.85635 590592.3877 77 69570.22 44294.42908 565316.5968 78 69570.22 42398.74476 538145.1215 79 69570.22 40360.88411 508935.7856 80 69570.22 38170.18392 477535.7496 81 69570.22 35815.18122 443780.7108 82 69570.22 33283.55331 407494.0441 83 69570.22 30562.05331 368485.8774 84 69570.22 27636.4408 326552.0982 85 69570.22 24491.40736 281473.2856 86 69570.22 21110.49642 233013.562 87 69570.22 17476.01715 180919.3591 88 69570.22 13568.95193 124918.0911 89 69570.22 9368.85683 64716.7279 90 69570.22 4853.754592 0

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