Question

you plan to retire in 35 years. during each year of retirement, you want to have an amount of money with the same prchaning powe that $50,000 has today. inflation is expected to be 3% per year form now.

A. how much money do you need in the first year of retiment (35 years from todya)? round to the nearest dollar.

B.  Ignore your answer to “a” and assume you need $125,000 in the first year of
retirement. Call it CF1. Note that you withdraw that money 35 years from today (t = 35). Now
assume you will keep your retirement savings (“nest egg”) in an investment that generates a
return of 4% per year, during each year of your retirement and in the year before it starts. You
plan to be retired for 27 years. You will continue to need the same purchasing power (during each
year of retirement) that $125,000 represents in the first year of retirement. Inflation will remain
at 3% per year forever. How much money do you need to have in your retirement account, one
year before your retirement starts (this helps with timing issues), to fund (or finance) this stream
of withdrawals [i.e. what is the nest egg size at t=34]? Round your final answer to the nearest
thousand dollars.

C.Ignore your answer to “b” and assume your nest egg size at [t = 34] is $5,000,000.
Also assume that you will save money in an investment that earns 7% per year until [t = 34], to
reach your goal. You will make your first savings payment (into the investment) in one year (CF1).
You will grow your annual payments by 2% per year. You will make 34 annual payments. How big
must your first savings payment be, to reach your goal?

Answer 1

For Part A

To have the same purchasing power of amount $ 50,000 after 35 years follow below principle to calculate figure -

Future Value = 50,000 (3% ; 35 Yrs) FVAT ( Future Value Annuity Factor)

= 50,000 * 2.814

= $ 1,40,700 (After 35 years you should have $ 1,40,700 to have same purchasing capacity as of today).

For Part B

Below Schedule will help you out to know the value of nest egg amount as of t 34 i.e.

Term	Yr	Nest Size Year-end	Earnings	Withdrawals	Present Value factor @ 4%	Present Value of Withdrawl
0	34	2,870,252			0.9615
1	35	2,860,062	114,810	125,000	1.0000	125,000
2	36	2,845,715	114,402	128,750	0.9615	123,798
3	37	2,826,931	113,829	132,613	0.9246	122,608
4	38	2,803,417	113,077	136,591	0.8890	121,429
5	39	2,774,865	112,137	140,689	0.8548	120,261
6	40	2,740,951	110,995	144,909	0.8219	119,105
7	41	2,701,332	109,638	149,257	0.7903	117,960
8	42	2,655,651	108,053	153,734	0.7599	116,825
9	43	2,603,531	106,226	158,346	0.7307	115,702
10	44	2,544,575	104,141	163,097	0.7026	114,590
11	45	2,478,369	101,783	167,990	0.6756	113,488
12	46	2,404,474	99,135	173,029	0.6496	112,396
13	47	2,322,433	96,179	178,220	0.6246	111,316
14	48	2,231,764	92,897	183,567	0.6006	110,245
15	49	2,131,961	89,271	189,074	0.5775	109,185
16	50	2,022,493	85,278	194,746	0.5553	108,136
17	51	1,902,805	80,900	200,588	0.5339	107,096
18	52	1,772,311	76,112	206,606	0.5134	106,066
19	53	1,630,399	70,892	212,804	0.4936	105,046
20	54	1,476,427	65,216	219,188	0.4746	104,036
21	55	1,309,720	59,057	225,764	0.4564	103,036
22	56	1,129,572	52,389	232,537	0.4388	102,045
23	57	935,242	45,183	239,513	0.4220	101,064
24	58	725,953	37,410	246,698	0.4057	100,092
25	59	500,892	29,038	254,099	0.3901	99,130
26	60	259,206	20,036	261,722	0.3751	98,176
27	61	0	10,368	269,574	0.3607	97,232

According to above schedule you should have $ 28,70,252 to withdraw amount of $ 1,25,000 along with inflation addition.