I have $500,000 in the bank now. I plan to withdraw $30,000 at the end of...

I have $500,000 in the bank now. I plan to withdraw $30,000 at the end of this year. Each subsequent end of year withdrawal will increase by 7%. If I earn 8% per year on my investments in the first 4 years, then 6% per year in the next 3 years, and 5% per year in the following 4 years,
1. Determine how much money I will have at the end of 11 years.
2. Determine the initial withdrawal amount at the end of this year that will leave me with no money at the end of 11 years using either Solver or Goal Seek.

Expert Solution

A.

Years	Total Amt.	Incremental Factor for Investment = 1+Rate of Interest	Amt. @ end of the year	Incremental Factor for Withdrawl = 1+Rate of Increase	Withdrawl @ end of the year	Net Amt. @ end of the year
1	500,000	1.08	540,000	1.00	30,000	510,000
2	510,000	1.08	550,800	1.07	32,100	518,700
3	518,700	1.08	560,196	1.07	34,347	525,849
4	525,849	1.08	567,917	1.07	36,751	531,166
5	531,166	1.06	563,036	1.07	39,324	523,712
6	523,712	1.06	555,134	1.07	42,077	513,058
7	513,058	1.06	543,841	1.07	45,022	498,819
8	498,819	1.05	523,760	1.07	48,173	475,587
9	475,587	1.05	499,366	1.07	51,546	447,821
10	447,821	1.05	470,212	1.07	55,154	415,058
11	415,058	1.05	435,811	1.07	59,015	376,796

B.

Using goal seek function as per below screenshot the answer will be $48,592

Years	Total Amt.	Incremental Factor for Investment = 1+Rate of Interest	Amt. @ end of the year	Incremental Factor for Withdrawl = 1+Rate of Increase	Withdrawl @ end of the year	Net Amt. @ end of the year
1	500,000	1.08	540,000	1.00	48,592	491,408
2	491,408	1.08	530,720	1.07	51,994	478,726
3	478,726	1.08	517,024	1.07	55,633	461,391
4	461,391	1.08	498,302	1.07	59,528	438,775
5	438,775	1.06	465,101	1.07	63,695	401,406
6	401,406	1.06	425,491	1.07	68,153	357,337
7	357,337	1.06	378,778	1.07	72,924	305,854
8	305,854	1.05	321,146	1.07	78,029	243,118
9	243,118	1.05	255,273	1.07	83,491	171,783
10	171,783	1.05	180,372	1.07	89,335	91,037
11	91,037	1.05	95,589	1.07	95,589	(0)

jeff jeffy answered 2 years ago

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