You hope to retire in 30 years, when you do, you would like to have the...

You hope to retire in 30 years, when you do, you would like to have the purchasing power of $100,000 today, during each year of retirement. Your cash is needed at the beginning of each year of retirement. Inflation is expected to be 3% per year from now until the end of your retirement. Your retirement will last 25 years, you expect your 401k to earn 5% per year during your retirement years. How much money do you need at the beginning of your retirement years, to “just meet” your retirement needs (i.e. what is the size of the needed nest egg)?

Expert Solution

ANSWER:

	5.00%	0
Cash flows	Year	Discounted CF
242,726.25	0	242726.25
250,008.03	1	238102.89
257,508.28	2	233567.60
265,233.52	3	229118.69
273,190.53	4	224754.52
281,386.25	5	220473.49
289,827.83	6	216273.99
298,522.67	7	212154.49
307,478.35	8	208113.45
316,702.70	9	204149.38
326,203.78	10	200260.82
335,989.89	11	196446.33
346,069.59	12	192704.50
356,451.68	13	189033.935
367,145.23	14	185433.288
378,159.58	15	181901.226
389,504.37	16	178436.441
401,189.50	17	175037.651
413,225.19	18	171703.601
425,621.94	19	168433.056
438,390.60	20	165224.807
451,542.32	21	162077.668
465,088.59	22	158990.474
479,041.25	23	155962.084
493,412.48	24	152991.378

at the 30th year amount needed = 1.03³⁰*100,000 = 242,726.25

each cash flow is discounted by 1.05ⁿ

Sum of discounted cash flows is the size of the needed nest egg

nest egg = 4,864,072.01

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