Suppose that you are 22 today and that your salary for the year ending today is
ID: 1170340 • Letter: S
Question
Suppose that you are 22 today and that your salary for the year ending today is $61,250. Suppose that you are paid on an annual basis at the end of each year; so you are receiving $61,250 today. You plan to retire at age 68and will need 75% of your last year’s salary for your annual living expenses starting at age 69. You have saved $50,000 to date. All living expenses between now and retirement will be covered by your annual salary in each year. All living expenses after retirement will be covered by your retirement income. Assume that your first withdrawal from your retirement account for post-retirement income occurs on your 69thbirthdayand that you next deposit into your retirement account will be one year from now. You have some older relatives that have always had an interest in you and have indicated that you are in their wills. Assume that you will inherit $100,000 when you turn 36. Assume also that, given the state of health care costs and a family history of healthcare issues, that you will need to have an amount of $1.25 million available by age 57 to cover healthcare costs above and beyond what your health insurance plan is likely to cover. Assume that you will save 10% of your annual income while you work, and that you will not save any additional amount after you retire. You project that your salary will grow at a rate of 5% and that your retirement income needs will grow at 3%to reflect long-term inflation forecasts. The higher growth rate in your salary reflects your expectation that you will receive promotions and that absent promotions your salary will keep pace with inflation. The appropriate interest rate for your working life is 9% and declines to 6% after you retire. How much will you have to leave to your heirs if you live to age 90?
Explanation / Answer
Number of years to retire 46 (68-22) Salary before retirement (Last Salary) $ 577,848 (61250*(1.05^46) First withdrawal age 69 $ 433,386 (0.75*577848) Salary at end of year 1 $ 64,313 (1.05*61250) Salary at end of year (N+1)=1.05*(Salary at end of year (N) Present Value(PV) of cash flow=(Cash flow)/((1+i)^N) i=Interest rate, N=Year of cash flow ANNUAL CASH FLOW IN SAVINGS ACCOUNT BEFORE RETIREMENT: Interest Rate=9%=0.09 N A B=0.1*A C D E=B+C+D F=E/(1.09^N) Age Year Salary Savings Inheritance Healthcare cost Net Savings PV of Savings 23 1 $ 64,313 $ 6,431 $ 6,431 $ 5,900 24 2 $ 67,528 $ 6,753 $ 6,753 $ 5,684 25 3 $ 70,905 $ 7,090 $ 7,090 $ 5,475 26 4 $ 74,450 $ 7,445 $ 7,445 $ 5,274 27 5 $ 78,172 $ 7,817 $ 7,817 $ 5,081 28 6 $ 82,081 $ 8,208 $ 8,208 $ 4,894 29 7 $ 86,185 $ 8,618 $ 8,618 $ 4,715 30 8 $ 90,494 $ 9,049 $ 9,049 $ 4,542 31 9 $ 95,019 $ 9,502 $ 9,502 $ 4,375 32 10 $ 99,770 $ 9,977 $ 9,977 $ 4,214 33 11 $ 104,758 $ 10,476 $ 10,476 $ 4,060 34 12 $ 109,996 $ 11,000 $ 11,000 $ 3,911 35 13 $ 115,496 $ 11,550 $ 11,550 $ 3,767 36 14 $ 121,271 $ 12,127 $100,000 $ 112,127 $ 33,554 37 15 $ 127,334 $ 12,733 $ 12,733 $ 3,496 38 16 $ 133,701 $ 13,370 $ 13,370 $ 3,368 39 17 $ 140,386 $ 14,039 $ 14,039 $ 3,244 40 18 $ 147,405 $ 14,741 $ 14,741 $ 3,125 41 19 $ 154,776 $ 15,478 $ 15,478 $ 3,010 42 20 $ 162,514 $ 16,251 $ 16,251 $ 2,900 43 21 $ 170,640 $ 17,064 $ 17,064 $ 2,793 44 22 $ 179,172 $ 17,917 $ 17,917 $ 2,691 45 23 $ 188,131 $ 18,813 $ 18,813 $ 2,592 46 24 $ 197,537 $ 19,754 $ 19,754 $ 2,497 47 25 $ 207,414 $ 20,741 $ 20,741 $ 2,405 48 26 $ 217,785 $ 21,778 $ 21,778 $ 2,317 49 27 $ 228,674 $ 22,867 $ 22,867 $ 2,232 50 28 $ 240,108 $ 24,011 $ 24,011 $ 2,150 51 29 $ 252,113 $ 25,211 $ 25,211 $ 2,071 52 30 $ 264,719 $ 26,472 $ 26,472 $ 1,995 53 31 $ 277,955 $ 27,795 $ 27,795 $ 1,922 54 32 $ 291,853 $ 29,185 $ 29,185 $ 1,851 55 33 $ 306,445 $ 30,645 $ 30,645 $ 1,784 56 34 $ 321,768 $ 32,177 $ 32,177 $ 1,718 57 35 $ 337,856 $ 33,786 ($1,250,000) $ (1,216,214) $ (59,578) 58 36 $ 354,749 $ 35,475 $ 35,475 $ 1,594 59 37 $ 372,486 $ 37,249 $ 37,249 $ 1,536 60 38 $ 391,110 $ 39,111 $ 39,111 $ 1,479 61 39 $ 410,666 $ 41,067 $ 41,067 $ 1,425 62 40 $ 431,199 $ 43,120 $ 43,120 $ 1,373 63 41 $ 452,759 $ 45,276 $ 45,276 $ 1,322 64 42 $ 475,397 $ 47,540 $ 47,540 $ 1,274 65 43 $ 499,167 $ 49,917 $ 49,917 $ 1,227 66 44 $ 524,125 $ 52,413 $ 52,413 $ 1,182 67 45 $ 550,332 $ 55,033 $ 55,033 $ 1,139 68 46 $ 577,848 $ 57,785 $ 57,785 $ 1,097 SUM $ 100,678 Present Value of net savings till retirement $ 100,678 Future Value of net savings at Retirement $ 5,303,380 (100678*(1.09^46) CASH FLOWS AFTER RETIREMENT Inflation rate=3% Withdrawal in year 2(Age70)=1.03*433386= $ 446,387.82 Withdrawal in year (N+1)=1.03*(Withdrawal in year (N+1) Interest rate=6%=0.06 N A B=A/(1.06^N) Age YEAR Withdrawal PV of Withdrawal 69 1 $ 433,386 $ 408,855 70 2 $ 446,388 $ 397,284 71 3 $ 459,779 $ 386,040 72 4 $ 473,573 $ 375,114 73 5 $ 487,780 $ 364,498 74 6 $ 502,413 $ 354,182 75 7 $ 517,486 $ 344,158 76 8 $ 533,010 $ 334,417 77 9 $ 549,001 $ 324,953 78 10 $ 565,471 $ 315,756 79 11 $ 582,435 $ 306,819 80 12 $ 599,908 $ 298,136 81 13 $ 617,905 $ 289,698 82 14 $ 636,442 $ 281,499 83 15 $ 655,536 $ 273,532 84 16 $ 675,202 $ 265,791 85 17 $ 695,458 $ 258,268 86 18 $ 716,321 $ 250,959 87 19 $ 737,811 $ 243,856 88 20 $ 759,945 $ 236,955 89 21 $ 782,744 $ 230,248 90 22 $ 806,226 $ 223,732 SUM $ 6,764,748 Present value at Retirement needed for living expenses $ 6,764,748 Amount available at retirement $ 5,303,380 Shortfall $ 1,461,368 PV of Amount of inheritance $ (1,461,368) Amount left at age 90 $ (5,266,093) (-1461368*(1.06^22)
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