Question

Todd and Jessalyn are 25, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $2400 per year to prepare for retirement. Jessalyn just told Todd, though, that she had heard that they would actually have more money the day they retire if they put $2400 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - than they would have if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do). a) How much money will Todd and Jessalyn have in 45 years if they put away $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust the 8.4% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal) example of rounding: .062134 = .06213 or 6.213%

b) If Todd and Jessalyn wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years in order to have $1,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

a)

Monthly rate	0.70%
Total months	540

Month	Amount invested	Remaining months	Value at the end
1	200	539	8,588.44669
2	200	538	8,528.74547
3	200	537	8,469.45925
4	200	536	8,410.58516
5	200	535	8,352.12031
6	200	534	8,294.06188
7	200	533	8,236.40703
8	200	532	8,179.15296
9	200	531	8,122.29688
10	200	530	8,065.83603
11	200	529	8,009.76766
12	200	528	7,954.08903
13	200	527	7,898.79745
14	200	526	7,843.89022
15	200	525	7,789.36467
16	200	524	7,735.21814
17	200	523	7,681.44801
18	200	522	7,628.05164
19	200	521	7,575.02646
20	200	520	7,522.36987
21	200	519	7,470.07931
22	200	518	7,418.15225
23	200	517	7,366.58615
24	200	516	7,315.37850
25	200	515	7,264.52681
26	200	514	7,214.02861
27	200	513	7,163.88144
28	200	512	7,114.08286
29	200	511	7,064.63044
30	200	510	7,015.52179
31	200	509	6,966.75451
32	200	508	6,918.32623
33	200	507	6,870.23458
34	200	506	6,822.47724
35	200	505	6,775.05188
36	200	504	6,727.95619
37	200	503	6,681.18787
38	200	502	6,634.74466
39	200	501	6,588.62429
40	200	500	6,542.82452
41	200	499	6,497.34312
42	200	498	6,452.17787
43	200	497	6,407.32659
44	200	496	6,362.78708
45	200	495	6,318.55718
46	200	494	6,274.63473
47	200	493	6,231.01761
48	200	492	6,187.70368
49	200	491	6,144.69085
50	200	490	6,101.97701
51	200	489	6,059.56009
52	200	488	6,017.43802
53	200	487	5,975.60876
54	200	486	5,934.07027
55	200	485	5,892.82052
56	200	484	5,851.85752
57	200	483	5,811.17927
58	200	482	5,770.78378
59	200	481	5,730.66910
60	200	480	5,690.83326
61	200	479	5,651.27434
62	200	478	5,611.99041
63	200	477	5,572.97955
64	200	476	5,534.23987
65	200	475	5,495.76949
66	200	474	5,457.56652
67	200	473	5,419.62912
68	200	472	5,381.95543
69	200	471	5,344.54363
70	200	470	5,307.39188
71	200	469	5,270.49839
72	200	468	5,233.86136
73	200	467	5,197.47901
74	200	466	5,161.34956
75	200	465	5,125.47127
76	200	464	5,089.84237
77	200	463	5,054.46114
78	200	462	5,019.32586
79	200	461	4,984.43482
80	200	460	4,949.78631
81	200	459	4,915.37866
82	200	458	4,881.21019
83	200	457	4,847.27924
84	200	456	4,813.58415
85	200	455	4,780.12328
86	200	454	4,746.89502
87	200	453	4,713.89773
88	200	452	4,681.12983
89	200	451	4,648.58970
90	200	450	4,616.27577
91	200	449	4,584.18646
92	200	448	4,552.32022
93	200	447	4,520.67549
94	200	446	4,489.25074
95	200	445	4,458.04443
96	200	444	4,427.05504
97	200	443	4,396.28107
98	200	442	4,365.72103
99	200	441	4,335.37341
100	200	440	4,305.23675
101	200	439	4,275.30959
102	200	438	4,245.59045
103	200	437	4,216.07791
104	200	436	4,186.77052
105	200	435	4,157.66685
106	200	434	4,128.76549
107	200	433	4,100.06503
108	200	432	4,071.56409
109	200	431	4,043.26126
110	200	430	4,015.15517
111	200	429	3,987.24446
112	200	428	3,959.52776
113	200	427	3,932.00374
114	200	426	3,904.67104
115	200	425	3,877.52834
116	200	424	3,850.57432
117	200	423	3,823.80767
118	200	422	3,797.22708
119	200	421	3,770.83126
120	200	420	3,744.61893
121	200	419	3,718.58881
122	200	418	3,692.73963
123	200	417	3,667.07014
124	200	416	3,641.57908
125	200	415	3,616.26523
126	200	414	3,591.12734
127	200	413	3,566.16419
128	200	412	3,541.37456
129	200	411	3,516.75726
130	200	410	3,492.31109
131	200	409	3,468.03484
132	200	408	3,443.92735
133	200	407	3,419.98744
134	200	406	3,396.21394
135	200	405	3,372.60570
136	200	404	3,349.16157
137	200	403	3,325.88041
138	200	402	3,302.76108
139	200	401	3,279.80246
140	200	400	3,257.00344
141	200	399	3,234.36290
142	200	398	3,211.87974
143	200	397	3,189.55287
144	200	396	3,167.38120
145	200	395	3,145.36366
146	200	394	3,123.49916
147	200	393	3,101.78666
148	200	392	3,080.22508
149	200	391	3,058.81339
150	200	390	3,037.55053
151	200	389	3,016.43548
152	200	388	2,995.46721
153	200	387	2,974.64470
154	200	386	2,953.96693
155	200	385	2,933.43290
156	200	384	2,913.04161
157	200	383	2,892.79207
158	200	382	2,872.68328
159	200	381	2,852.71428
160	200	380	2,832.88409
161	200	379	2,813.19175
162	200	378	2,793.63630
163	200	377	2,774.21678
164	200	376	2,754.93225
165	200	375	2,735.78178
166	200	374	2,716.76443
167	200	373	2,697.87928
168	200	372	2,679.12540
169	200	371	2,660.50189
170	200	370	2,642.00783
171	200	369	2,623.64233
172	200	368	2,605.40450
173	200	367	2,587.29345
174	200	366	2,569.30829
175	200	365	2,551.44815
176	200	364	2,533.71217
177	200	363	2,516.09947
178	200	362	2,498.60921
179	200	361	2,481.24052
180	200	360	2,463.99258
181	200	359	2,446.86452
182	200	358	2,429.85554
183	200	357	2,412.96478
184	200	356	2,396.19144
185	200	355	2,379.53470
186	200	354	2,362.99374
187	200	353	2,346.56777
188	200	352	2,330.25598
189	200	351	2,314.05757
190	200	350	2,297.97177
191	200	349	2,281.99779
192	200	348	2,266.13484
193	200	347	2,250.38217
194	200	346	2,234.73899
195	200	345	2,219.20456
196	200	344	2,203.77812
197	200	343	2,188.45890
198	200	342	2,173.24618
199	200	341	2,158.13921
200	200	340	2,143.13725
201	200	339	2,128.23957
202	200	338	2,113.44545
203	200	337	2,098.75417
204	200	336	2,084.16502
205	200	335	2,069.67727
206	200	334	2,055.29024
207	200	333	2,041.00322
208	200	332	2,026.81551
209	200	331	2,012.72643
210	200	330	1,998.73528
211	200	329	1,984.84139
212	200	328	1,971.04408
213	200	327	1,957.34268
214	200	326	1,943.73653
215	200	325	1,930.22495
216	200	324	1,916.80730
217	200	323	1,903.48292
218	200	322	1,890.25116
219	200	321	1,877.11138
220	200	320	1,864.06294
221	200	319	1,851.10521
222	200	318	1,838.23754
223	200	317	1,825.45933
224	200	316	1,812.76994
225	200	315	1,800.16876
226	200	314	1,787.65517
227	200	313	1,775.22857
228	200	312	1,762.88835
229	200	311	1,750.63392
230	200	310	1,738.46466
231	200	309	1,726.38000
232	200	308	1,714.37935
233	200	307	1,702.46211
234	200	306	1,690.62772
235	200	305	1,678.87559
236	200	304	1,667.20515
237	200	303	1,655.61584
238	200	302	1,644.10709
239	200	301	1,632.67834
240	200	300	1,621.32904
241	200	299	1,610.05863
242	200	298	1,598.86656
243	200	297	1,587.75230
244	200	296	1,576.71529
245	200	295	1,565.75501
246	200	294	1,554.87091
247	200	293	1,544.06247
248	200	292	1,533.32917
249	200	291	1,522.67048
250	200	290	1,512.08587
251	200	289	1,501.57485
252	200	288	1,491.13689
253	200	287	1,480.77149
254	200	286	1,470.47814
255	200	285	1,460.25635
256	200	284	1,450.10561
257	200	283	1,440.02543
258	200	282	1,430.01533
259	200	281	1,420.07480
260	200	280	1,410.20338
261	200	279	1,400.40057
262	200	278	1,390.66591
263	200	277	1,380.99892
264	200	276	1,371.39913
265	200	275	1,361.86606
266	200	274	1,352.39927
267	200	273	1,342.99828
268	200	272	1,333.66264
269	200	271	1,324.39190
270	200	270	1,315.18560
271	200	269	1,306.04330
272	200	268	1,296.96455
273	200	267	1,287.94890
274	200	266	1,278.99593
275	200	265	1,270.10519
276	200	264	1,261.27626
277	200	263	1,252.50870
278	200	262	1,243.80209
279	200	261	1,235.15599
280	200	260	1,226.57000
281	200	259	1,218.04370
282	200	258	1,209.57666
283	200	257	1,201.16848
284	200	256	1,192.81875
285	200	255	1,184.52706
286	200	254	1,176.29301
287	200	253	1,168.11620
288	200	252	1,159.99622
289	200	251	1,151.93269
290	200	250	1,143.92522
291	200	249	1,135.97340
292	200	248	1,128.07687
293	200	247	1,120.23522
294	200	246	1,112.44808
295	200	245	1,104.71508
296	200	244	1,097.03583
297	200	243	1,089.40996
298	200	242	1,081.83710
299	200	241	1,074.31688
300	200	240	1,066.84894
301	200	239	1,059.43291
302	200	238	1,052.06843
303	200	237	1,044.75514
304	200	236	1,037.49269
305	200	235	1,030.28073
306	200	234	1,023.11889
307	200	233	1,016.00685
308	200	232	1,008.94424
309	200	231	1,001.93072
310	200	230	994.96596
311	200	229	988.04961
312	200	228	981.18134
313	200	227	974.36082
314	200	226	967.58770
315	200	225	960.86167
316	200	224	954.18240
317	200	223	947.54955
318	200	222	940.96281
319	200	221	934.42186
320	200	220	927.92637
321	200	219	921.47604
322	200	218	915.07055
323	200	217	908.70958
324	200	216	902.39283
325	200	215	896.11999
326	200	214	889.89075
327	200	213	883.70482
328	200	212	877.56189
329	200	211	871.46165
330	200	210	865.40383
331	200	209	859.38811
332	200	208	853.41421
333	200	207	847.48184
334	200	206	841.59070
335	200	205	835.74052
336	200	204	829.93100
337	200	203	824.16187
338	200	202	818.43284
339	200	201	812.74363
340	200	200	807.09398
341	200	199	801.48359
342	200	198	795.91221
343	200	197	790.37955
344	200	196	784.88535
345	200	195	779.42935
346	200	194	774.01127
347	200	193	768.63085
348	200	192	763.28784
349	200	191	757.98196
350	200	190	752.71297
351	200	189	747.48061
352	200	188	742.28462
353	200	187	737.12474
354	200	186	732.00074
355	200	185	726.91235
356	200	184	721.85934
357	200	183	716.84145
358	200	182	711.85844
359	200	181	706.91007
360	200	180	701.99609
361	200	179	697.11628
362	200	178	692.27039
363	200	177	687.45818
364	200	176	682.67942
365	200	175	677.93389
366	200	174	673.22134
367	200	173	668.54155
368	200	172	663.89429
369	200	171	659.27933
370	200	170	654.69646
371	200	169	650.14544
372	200	168	645.62606
373	200	167	641.13809
374	200	166	636.68132
375	200	165	632.25553
376	200	164	627.86051
377	200	163	623.49603
378	200	162	619.16190
379	200	161	614.85790
380	200	160	610.58381
381	200	159	606.33943
382	200	158	602.12456
383	200	157	597.93899
384	200	156	593.78251
385	200	155	589.65493
386	200	154	585.55603
387	200	153	581.48563
388	200	152	577.44353
389	200	151	573.42952
390	200	150	569.44342
391	200	149	565.48502
392	200	148	561.55415
393	200	147	557.65059
394	200	146	553.77417
395	200	145	549.92470
396	200	144	546.10199
397	200	143	542.30584
398	200	142	538.53609
399	200	141	534.79254
400	200	140	531.07502
401	200	139	527.38334
402	200	138	523.71731
403	200	137	520.07678
404	200	136	516.46155
405	200	135	512.87145
406	200	134	509.30630
407	200	133	505.76594
408	200	132	502.25019
409	200	131	498.75888
410	200	130	495.29183
411	200	129	491.84889
412	200	128	488.42988
413	200	127	485.03464
414	200	126	481.66300
415	200	125	478.31480
416	200	124	474.98987
417	200	123	471.68805
418	200	122	468.40919
419	200	121	465.15311
420	200	120	461.91968
421	200	119	458.70872
422	200	118	455.52007
423	200	117	452.35360
424	200	116	449.20914
425	200	115	446.08653
426	200	114	442.98563
427	200	113	439.90629
428	200	112	436.84835
429	200	111	433.81167
430	200	110	430.79609
431	200	109	427.80148
432	200	108	424.82769
433	200	107	421.87457
434	200	106	418.94197
435	200	105	416.02977
436	200	104	413.13780
437	200	103	410.26594
438	200	102	407.41404
439	200	101	404.58197
440	200	100	401.76958
441	200	99	398.97674
442	200	98	396.20332
443	200	97	393.44918
444	200	96	390.71418
445	200	95	387.99819
446	200	94	385.30108
447	200	93	382.62272
448	200	92	379.96298
449	200	91	377.32173
450	200	90	374.69884
451	200	89	372.09418
452	200	88	369.50762
453	200	87	366.93905
454	200	86	364.38833
455	200	85	361.85535
456	200	84	359.33997
457	200	83	356.84207
458	200	82	354.36154
459	200	81	351.89825
460	200	80	349.45209
461	200	79	347.02293
462	200	78	344.61065
463	200	77	342.21515
464	200	76	339.83629
465	200	75	337.47398
466	200	74	335.12808
467	200	73	332.79849
468	200	72	330.48509
469	200	71	328.18778
470	200	70	325.90643
471	200	69	323.64095
472	200	68	321.39121
473	200	67	319.15711
474	200	66	316.93854
475	200	65	314.73539
476	200	64	312.54756
477	200	63	310.37493
478	200	62	308.21741
479	200	61	306.07489
480	200	60	303.94726
481	200	59	301.83442
482	200	58	299.73626
483	200	57	297.65269
484	200	56	295.58361
485	200	55	293.52891
486	200	54	291.48849
487	200	53	289.46225
488	200	52	287.45010
489	200	51	285.45194
490	200	50	283.46766
491	200	49	281.49718
492	200	48	279.54040
493	200	47	277.59722
494	200	46	275.66755
495	200	45	273.75129
496	200	44	271.84835
497	200	43	269.95864
498	200	42	268.08206
499	200	41	266.21853
500	200	40	264.36796
501	200	39	262.53025
502	200	38	260.70531
503	200	37	258.89306
504	200	36	257.09340
505	200	35	255.30626
506	200	34	253.53154
507	200	33	251.76916
508	200	32	250.01902
509	200	31	248.28106
510	200	30	246.55517
511	200	29	244.84128
512	200	28	243.13931
513	200	27	241.44916
514	200	26	239.77077
515	200	25	238.10404
516	200	24	236.44890
517	200	23	234.80526
518	200	22	233.17305
519	200	21	231.55218
520	200	20	229.94258
521	200	19	228.34417
522	200	18	226.75688
523	200	17	225.18061
524	200	16	223.61530
525	200	15	222.06088
526	200	14	220.51726
527	200	13	218.98437
528	200	12	217.46213
529	200	11	215.95048
530	200	10	214.44933
531	200	9	212.95862
532	200	8	211.47828
533	200	7	210.00822
534	200	6	208.54838
535	200	5	207.09869
536	200	4	205.65907
537	200	3	204.22947
538	200	2	202.80980
539	200	1	201.40000
540	200	0	200.00000
		Total	12,06,938

b)

Yearly rate	8.40%
No. of years	20
Year	Years remaining	Compounded rate
1	19	4.629737437
2	18	4.270975495
3	17	3.940014294
4	16	3.634699533
5	15	3.35304385
6	14	3.093213884
7	13	2.853518343
8	12	2.632396995
9	11	2.428410512
10	10	2.2402311
11	9	2.066633856
12	8	1.906488797
13	7	1.758753503
14	6	1.622466331
15	5	1.496740158
16	4	1.380756603
17	3	1.273760704
18	2	1.175056
19	1	1.084
20	0	1
	Total compounded rate	47.8408974

Therefore, (amount invested/year) * 47.8409 = $1,000,000

Amount invested/year = $20,902.62

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