Question

You are planning to save for your retirement in 35 years and the college tuition for your two children. Your current monthly salary is $9,000 per month and you expect your salary to keep pace with inflation. You expect inflation to be a 3.5 percent EAR for the rest of your life. You plan to deposit 12 percent of your salary each month into a retirement account. Additionally, your employer will deposit 4 percent of your salary into the account. You expect to earn a 10.8 nominal nominal EAR in your retirement savings account until retirement. Your children will begin college 15 years and 17 years from now. The university that you plan for your children to attend has started a new legacy program where for a minimal donation today, the school will guarantee that the tuition for your first child will be $130,000 and the tuition for your second child will be $135,000. Each of these tuition payments will be made when your child starts college and will cover the entire four years of tuition. If you can earn an 8.7 percent EAR after you retire, how much can you withdraw each month in real terms for the 25 years of your retirement?

Answer 1

We need to calculate future value of this fund 35 years from now.
Annual salary at beginning is 9000*12 = 108,000 and this will grow at the rate of 3.5%
Year	Salary	Contribution to fund @ 12%	Employer Contribution @ 4%	Total Contribution	Expected outflow	Net Contribution/Withdrawal	Rate of Interest	Discounting Factor	Future Value
1	108,000	12,960	4,320	17,280	-	17,280	10.80%	32.69	564,801
2	111,780	13,414	4,471	17,885	-	17,885	10.80%	29.50	527,590
3	115,692	13,883	4,628	18,511	-	18,511	10.80%	26.62	492,830
4	119,742	14,369	4,790	19,159	-	19,159	10.80%	24.03	460,360
5	123,932	14,872	4,957	19,829	-	19,829	10.80%	21.69	430,029
6	128,270	15,392	5,131	20,523	-	20,523	10.80%	19.57	401,697
7	132,760	15,931	5,310	21,242	-	21,242	10.80%	17.66	375,231
8	137,406	16,489	5,496	21,985	-	21,985	10.80%	15.94	350,509
9	142,215	17,066	5,689	22,754	-	22,754	10.80%	14.39	327,416
10	147,193	17,663	5,888	23,551	-	23,551	10.80%	12.99	305,845
11	152,345	18,281	6,094	24,375	-	24,375	10.80%	11.72	285,694
12	157,677	18,921	6,307	25,228	-	25,228	10.80%	10.58	266,871
13	163,195	19,583	6,528	26,111	-	26,111	10.80%	9.55	249,289
14	168,907	20,269	6,756	27,025	-	27,025	10.80%	8.62	232,864
15	174,819	20,978	6,993	27,971	130,000	(102,029)	10.80%	7.78	(793,448)
16	180,938	21,713	7,238	28,950	-	28,950	10.80%	7.02	203,191
17	187,270	22,472	7,491	29,963	135,000	(105,037)	10.80%	6.33	(665,360)
18	193,825	23,259	7,753	31,012	-	31,012	10.80%	5.72	177,299
19	200,609	24,073	8,024	32,097	-	32,097	10.80%	5.16	165,617
20	207,630	24,916	8,305	33,221	-	33,221	10.80%	4.66	154,706
21	214,897	25,788	8,596	34,384	-	34,384	10.80%	4.20	144,513
22	222,419	26,690	8,897	35,587	-	35,587	10.80%	3.79	134,992
23	230,203	27,624	9,208	36,833	-	36,833	10.80%	3.42	126,098
24	238,260	28,591	9,530	38,122	-	38,122	10.80%	3.09	117,790
25	246,599	29,592	9,864	39,456	-	39,456	10.80%	2.79	110,030
26	255,230	30,628	10,209	40,837	-	40,837	10.80%	2.52	102,780
27	264,164	31,700	10,567	42,266	-	42,266	10.80%	2.27	96,009
28	273,409	32,809	10,936	43,745	-	43,745	10.80%	2.05	89,683
29	282,979	33,957	11,319	45,277	-	45,277	10.80%	1.85	83,775
30	292,883	35,146	11,715	46,861	-	46,861	10.80%	1.67	78,255
31	303,134	36,376	12,125	48,501	-	48,501	10.80%	1.51	73,099
32	313,743	37,649	12,550	50,199	-	50,199	10.80%	1.36	68,283
33	324,724	38,967	12,989	51,956	-	51,956	10.80%	1.23	63,784
34	336,090	40,331	13,444	53,774	-	53,774	10.80%	1.11	59,582
35	347,853	41,742	13,914	55,656	-	55,656	10.80%	1.00	55,656
								Future Value of Fund	5,917,362
This will be the total fund amount at retirement for which we need to withdraw each month for 25 years I.e. 25*12 = 300months
Nominal interest rate for this fund is 8.7% and inflation is 3.5% which means real interest rate is 5.2%
Monthly interest rate will be 5.2/12 = 0.433%
Now, using Financial calculator we will out :-
PV -	5,917,362
FV -	0
N -	300
I/Y	0.43%
Compute PMT		($35,271.39)