Question

Decision #2: Planning for Retirement

Erich and Mallory are 22, 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 $3000 per year to prepare for retirement. Mallory just told Erich, though, that she had heard that they would actually have more money the day they retire if they put $3000 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).   Please help Erich and Mallory make an informed decision:   

Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.2% annually.  

(Please do NOT ROUND when entering “Rates” for any of the questions below)

1. How much money will Erich and Mallory have in 45 years if they do nothing for the next 10 years, then put $3000 per year away for the remaining 35 years?

2. How much money will Erich and Mallory have in 10 years if they put $3000 per year away for the next 10 years?

b2) How much will the amount you just computed grow to if it remains invested for the remaining

35 years, but without any additional yearly deposits being made?

3. How much money will Erich and Mallory have in 45 years if they put $3000 per year away for each of the next 45 years?

How much money will Erich and Mallory have in 45 years if they put away $250

4. per MONTH at the end of each month for the next 45 years? (Remember to adjust 7.2% annual rate to a Rate per month!)

5. If Erich and Mallory 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

So answering your first question, f they ideally do nothing for 10 years and invest for rest of 35 years from the 45 years than the total amount which they will get is as shown in below table

• So the amount that Erich and Malory would get after 45 years and investing for 35 years with 10 years doing nothing would be $464,430.9116
• In ten years they will have $44,855.66749

If they invest for staring ten years and keep the amount for next 35 years then the amount would be as shown in below table

Yearly amount invested	Cumulative amount ( Interest + Outstanding )	Rate of return	Interest amount	Compounded amount
3000	-	7.2	216	3216
3000	6216	7.2	447.552	6663.552
3000	9663.552	7.2	695.775744	10359.32774
3000	13359.32774	7.2	961.8715976	14321.19934
3000	17321.19934	7.2	1247.126353	18568.32569
3000	21568.32569	7.2	1552.91945	23121.24514
3000	26121.24514	7.2	1880.72965	28001.97479
3000	31001.97479	7.2	2232.142185	33234.11698
3000	36234.11698	7.2	2608.856423	38842.9734
3000	41842.9734	7.2	3012.694085	44855.66749
0	44855.66749	7.2	3229.608059	48085.27555
0	48085.27555	7.2	3462.139839	51547.41539
0	51547.41539	7.2	3711.413908	55258.82929
0	55258.82929	7.2	3978.635709	59237.465
0	59237.465	7.2	4265.09748	63502.56248
0	63502.56248	7.2	4572.184499	68074.74698
0	68074.74698	7.2	4901.381783	72976.12876
0	72976.12876	7.2	5254.281271	78230.41004
0	78230.41004	7.2	5632.589523	83862.99956
0	83862.99956	7.2	6038.135968	89901.13553
0	89901.13553	7.2	6472.881758	96374.01728
0	96374.01728	7.2	6938.929244	103312.9465
0	103312.9465	7.2	7438.53215	110751.4787
0	110751.4787	7.2	7974.106465	118725.5851
0	118725.5851	7.2	8548.24213	127273.8273
0	127273.8273	7.2	9163.715564	136437.5428
0	136437.5428	7.2	9823.503084	146261.0459
0	146261.0459	7.2	10530.79531	156791.8412
0	156791.8412	7.2	11289.01257	168080.8538
0	168080.8538	7.2	12101.82147	180182.6753
0	180182.6753	7.2	12973.15262	193155.8279
0	193155.8279	7.2	13907.21961	207063.0475
0	207063.0475	7.2	14908.53942	221971.5869
0	221971.5869	7.2	15981.95426	237953.5412
0	237953.5412	7.2	17132.65496	255086.1961
0	255086.1961	7.2	18366.20612	273452.4023
0	273452.4023	7.2	19688.57296	293140.9752
0	293140.9752	7.2	21106.15022	314247.1254
0	314247.1254	7.2	22625.79303	336872.9185
0	336872.9185	7.2	24254.85013	361127.7686
0	361127.7686	7.2	26001.19934	387128.9679
0	387128.9679	7.2	27873.28569	415002.2536
0	415002.2536	7.2	29880.16226	444882.4159
0	444882.4159	7.2	32031.53394	476913.9498
0	476913.9498	7.2	34337.80439	511251.7542

• If they invest for starting 10 years and if they keep that amount for next 35 years than the amount would be computed to $511,251.7542

If they invest $3000 yearly for next 45 years than the amount would be as shown in below table

Yearly amount invested	Cumulative amount ( Interest + Outstanding )	Rate of return	Interest amount	Compounded amount
3000	-	7.2	216	3216
3000	6216	7.2	447.552	6663.552
3000	9663.552	7.2	695.775744	10359.32774
3000	13359.32774	7.2	961.8715976	14321.19934
3000	17321.19934	7.2	1247.126353	18568.32569
3000	21568.32569	7.2	1552.91945	23121.24514
3000	26121.24514	7.2	1880.72965	28001.97479
3000	31001.97479	7.2	2232.142185	33234.11698
3000	36234.11698	7.2	2608.856423	38842.9734
3000	41842.9734	7.2	3012.694085	44855.66749
3000	47855.66749	7.2	3445.608059	51301.27555
3000	54301.27555	7.2	3909.691839	58210.96739
3000	61210.96739	7.2	4407.189652	65618.15704
3000	68618.15704	7.2	4940.507307	73558.66434
3000	76558.66434	7.2	5512.223833	82070.88818
3000	85070.88818	7.2	6125.103949	91195.99213
3000	94195.99213	7.2	6782.111433	100978.1036
3000	103978.1036	7.2	7486.423456	111464.527
3000	114464.527	7.2	8241.445945	122705.973
3000	125705.973	7.2	9050.830053	134756.803
3000	137756.803	7.2	9918.489817	147675.2928
3000	150675.2928	7.2	10848.62108	161523.9139
3000	164523.9139	7.2	11845.7218	176369.6357
3000	179369.6357	7.2	12914.61377	192284.2495
3000	195284.2495	7.2	14060.46596	209344.7155
3000	212344.7155	7.2	15288.81951	227633.535
3000	230633.535	7.2	16605.61452	247239.1495
3000	250239.1495	7.2	18017.21876	268256.3682
3000	271256.3682	7.2	19530.45851	290786.8268
3000	293786.8268	7.2	21152.65153	314939.4783
3000	317939.4783	7.2	22891.64244	340831.1207
3000	343831.1207	7.2	24755.84069	368586.9614
3000	371586.9614	7.2	26754.26122	398341.2226
3000	401341.2226	7.2	28896.56803	430237.7907
3000	433237.7907	7.2	31193.12093	464430.9116
3000	467430.9116	7.2	33655.02563	501085.9372
3000	504085.9372	7.2	36294.18748	540380.1247
3000	543380.1247	7.2	39123.36898	582503.4937
3000	585503.4937	7.2	42156.25155	627659.7452
3000	630659.7452	7.2	45407.50166	676067.2469
3000	679067.2469	7.2	48892.84178	727960.0887
3000	730960.0887	7.2	52629.12638	783589.215
3000	786589.215	7.2	56634.42348	843223.6385
3000	846223.6385	7.2	60928.10197	907151.7405
3000	910151.7405	7.2	65530.92532	975682.6658

• The amount would be $975,682.6658

-- If they invest monthly 250 which is yearly 3000 for next 45 years than the amount would be same $975,682.6658 as the rate of return is calculate yearly

For last question I am unable to provide table however if they want to have $1,000,000 after 45years and investing only for 20 years

Then they need to invest yearly 22262.329