Question

Grady​ Zebrowski, age​ 25, just graduated from​ college, accepted his first job with a $47,000 ​salary, and is already looking forward to retirement in 40 years. He assumes a 2.1 percent inflation rate and plans to live in retirement for 20 years. He does not want to plan on any Social Security benefits. Assume Grady can earn a 9 percent rate of return on his investments prior to retirement and a 5 percent rate of return on his investments​ post-retirement to answer the following questions using your financial calculator.

a.  Grady wants to replace 90 percent of his current net income. What is his annual need in​ today's dollars?

b.  Grady thinks he might have an average tax rate of 13 percent at retirement if he is married. Adjusting for​ taxes, how much does Grady really need per​ year, in​ today's dollars?

c.  Adjusting for​ inflation, how much does Grady need per year in future dollars when he begins retirement in 40 years?

d.  If he needs this amount for 20 years, how much does he need in total for​ retirement?​ (Hint: Use the​ inflation-adjusted rate of​ return.)

e.  How much does Grady need to save per month to reach his retirement goal assuming he does not receive any employer match on his retirement​savings?

Answer 1

Q.1 - Grady wants to replace 90 percent of his current net income. What is his annual need in today's dollars?

Current Income = $ 47000

Annual Need in Today's Dollar= 90% of Current Income = 47000*90 = $ 42,300

Q.2 Grady thinks he might have an average tax rate of 13 percent at retirement if he is married. Adjusting for taxes, how much does Grady really need per year, in today's dollars?

Grady really need per year, in today's dollars = Annual Need in Today's Dollar/ (1-tax rate) = 42300/(1-.13) = $ 48620.69

Q.3 Adjusting for inflation, how much does Grady need per year in future dollars when he begins retirement in 40 years for the next 20 years using Future Value = PV*(1+Inlation Rate)^Period

Period	PV Tax Adjusted	Inflation Rate	Period	Future Dollars
Retirement Year 1	48620.69	2.10%	40	111647.96
Retirement Year 2	48620.69	2.10%	41	113992.57
Retirement Year 3	48620.69	2.10%	42	116386.41
Retirement Year 4	48620.69	2.10%	43	118830.53
Retirement Year 5	48620.69	2.10%	44	121325.97
Retirement Year 6	48620.69	2.10%	45	123873.81
Retirement Year 7	48620.69	2.10%	46	126475.16
Retirement Year 8	48620.69	2.10%	47	129131.14
Retirement Year 9	48620.69	2.10%	48	131842.90
Retirement Year 10	48620.69	2.10%	49	134611.60
Retirement Year 11	48620.69	2.10%	50	137438.44
Retirement Year 12	48620.69	2.10%	51	140324.65
Retirement Year 13	48620.69	2.10%	52	143271.47
Retirement Year 14	48620.69	2.10%	53	146280.17
Retirement Year 15	48620.69	2.10%	54	149352.05
Retirement Year 16	48620.69	2.10%	55	152488.44
Retirement Year 17	48620.69	2.10%	56	155690.70
Retirement Year 18	48620.69	2.10%	57	158960.21
Retirement Year 19	48620.69	2.10%	58	162298.37
Retirement Year 20	48620.69	2.10%	59	165706.64