Question

We will do one more quick retirement account analysis problem to see the impact of: (1) trying to save either a fixed amount each year or a constant percentage of your salary each year and (2) starting your retirement saving immediately or waiting 10 years to really start your retirement savings. Let’s assume that you put a savings deposit into your 401k account at the end of each year by saving money over that previous year period (i.e. so I normally think of them as beginning of year transactions for my cash flow table since I think of the “Period” column in my present value table as “time elapsed between time zero (e.g. today or whenever the cash flow table starts) and when the cash flow will take place.” (e.g. a cash flow in the row labelled “Period 1” occurs at the end of Year 0 or beginning of Year 1, so 1 years time has elapsed since “time 0”) Assume you graduate with your B.S. in Chemical Engineering in Spring semester 2023, take few months off to travel around Europe, and then start work in January 2024 with a starting salary of $70,000. You can also assume where it becomes important that you get an average yearly raise of 2% each year (i.e. so you make $70,000 your first year on the job, $71,400 your second year, etc.). Assume that you are going to retire 40 years later in January 2064. Assume that you are going to live the average of 20 years into retirement, i.e. that you will die in January 2084, and that you want to pay yourself $100,000 per year in retirement income each year, and that both while saving and throughout retirement that your 401k earns 7% in effective interest compounded yearly. Case 1: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you start saving with your first deposit at the end of 2024, how much would you have to save each year into your retirement account if you wanted to save the exact same amount each year? Case 2: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you start saving with your first deposit at the end of 2024, how much would you have to save each year on a percentage of your salary basis into your retirement account if you wanted to save the exact same percentage of your salary each year you are working (HINT: Here you may want to add a column to your cash flow table to track your yearly salary as it increase due to raises)? Case 3: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you have fun in your 20’s and early 30’s and wait to start saving with your first deposit at the end of 2034 (i.e. so now retirement is only 30 years after you start saving), how much would you have to save each year into your retirement account if you wanted to save the exact same amount each year? Write a short discussion of how you feel about your ability to achieve these types of retirement goals and savings and comment on the effect of waiting to start saving for retirement.

Answer 1

1)

PMT	100000
FV2084	0
n	20
r	7%
FV2064	?
FV2064	($1,133,559.52)
PV	0
r	7%
n	40
Saving p.a.	$5,306.69

Year		Opening balance	Interest@ 7%	Savings	Closing balance
2024
2025	1	$0.00	$371.47	$5,306.69	$5,678.16
2026	2	$5,678.16	$768.94	$5,306.69	$11,753.79
2027	3	$11,753.79	$1,194.23	$5,306.69	$18,254.71
2028	4	$18,254.71	$1,649.30	$5,306.69	$25,210.69
2029	5	$25,210.69	$2,136.22	$5,306.69	$32,653.60
2030	6	$32,653.60	$2,657.22	$5,306.69	$40,617.51
2031	7	$40,617.51	$3,214.69	$5,306.69	$49,138.89
2032	8	$49,138.89	$3,811.19	$5,306.69	$58,256.77
2033	9	$58,256.77	$4,449.44	$5,306.69	$68,012.90
2034	10	$68,012.90	$5,132.37	$5,306.69	$78,451.96
2035	11	$78,451.96	$5,863.11	$5,306.69	$89,621.76
2036	12	$89,621.76	$6,644.99	$5,306.69	$101,573.44
2037	13	$101,573.44	$7,481.61	$5,306.69	$114,361.73
2038	14	$114,361.73	$8,376.79	$5,306.69	$128,045.21
2039	15	$128,045.21	$9,334.63	$5,306.69	$142,686.53
2040	16	$142,686.53	$10,359.53	$5,306.69	$158,352.75
2041	17	$158,352.75	$11,456.16	$5,306.69	$175,115.60
2042	18	$175,115.60	$12,629.56	$5,306.69	$193,051.85
2043	19	$193,051.85	$13,885.10	$5,306.69	$212,243.63
2044	20	$212,243.63	$15,228.52	$5,306.69	$232,778.84
2045	21	$232,778.84	$16,665.99	$5,306.69	$254,751.52
2046	22	$254,751.52	$18,204.07	$5,306.69	$278,262.28
2047	23	$278,262.28	$19,849.83	$5,306.69	$303,418.80
2048	24	$303,418.80	$21,610.78	$5,306.69	$330,336.27
2049	25	$330,336.27	$23,495.01	$5,306.69	$359,137.97
2050	26	$359,137.97	$25,511.13	$5,306.69	$389,955.79
2051	27	$389,955.79	$27,668.37	$5,306.69	$422,930.85
2052	28	$422,930.85	$29,976.63	$5,306.69	$458,214.16
2053	29	$458,214.16	$32,446.46	$5,306.69	$495,967.31
2054	30	$495,967.31	$35,089.18	$5,306.69	$536,363.18
2055	31	$536,363.18	$37,916.89	$5,306.69	$579,586.76
2056	32	$579,586.76	$40,942.54	$5,306.69	$625,835.99
2057	33	$625,835.99	$44,179.99	$5,306.69	$675,322.67
2058	34	$675,322.67	$47,644.06	$5,306.69	$728,273.41
2059	35	$728,273.41	$51,350.61	$5,306.69	$784,930.71
2060	36	$784,930.71	$55,316.62	$5,306.69	$845,554.02
2061	37	$845,554.02	$59,560.25	$5,306.69	$910,420.95
2062	38	$910,420.95	$64,100.94	$5,306.69	$979,828.58
2063	39	$979,828.58	$68,959.47	$5,306.69	$1,054,094.74
2064	40	$1,054,094.74	$74,158.10	$5,306.69	$1,133,559.52
Year		Opening balance	Interest@ 7%	Retirement Income	Closing balance
2065	1	$1,133,559.52		-100000	$1,033,559.52
2066	2	$1,033,559.52	$72,349.17	-100000	$1,005,908.69
2067	3	$1,005,908.69	$70,413.61	-100000	$976,322.30
2068	4	$976,322.30	$68,342.56	-100000	$944,664.86
2069	5	$944,664.86	$66,126.54	-100000	$910,791.40
2070	6	$910,791.40	$63,755.40	-100000	$874,546.80
2071	7	$874,546.80	$61,218.28	-100000	$835,765.07
2072	8	$835,765.07	$58,503.56	-100000	$794,268.63
2073	9	$794,268.63	$55,598.80	-100000	$749,867.43
2074	10	$749,867.43	$52,490.72	-100000	$702,358.15
2075	11	$702,358.15	$49,165.07	-100000	$651,523.22
2076	12	$651,523.22	$45,606.63	-100000	$597,129.85
2077	13	$597,129.85	$41,799.09	-100000	$538,928.94
2078	14	$538,928.94	$37,725.03	-100000	$476,653.97
2079	15	$476,653.97	$33,365.78	-100000	$410,019.74
2080	16	$410,019.74	$28,701.38	-100000	$338,721.13
2081	17	$338,721.13	$23,710.48	-100000	$262,431.60
2082	18	$262,431.60	$18,370.21	-100000	$180,801.82
2083	19	$180,801.82	$12,656.13	-100000	$93,457.94
2084	20	$93,457.94	$6,542.06	-100000	$0.00

2)

PMT	100000
FV2084	0
n	20
r	7%
FV2064	?
FV2064	($1,133,559.52)
PV	2
r	7%
n	40
Saving %.

2)

1133559= x*382.87598

x=2960

%= 2960/70000

=4.2295%

=4.2295*1,02= 4.3141%

3)

PMT	100000
FV2084	0
n	20
r	7%
FV2064	?
FV2064	($1,133,559.52)
PV	2
r	7%
n	30
Saving p.a.	$12,000.16