Mathematical Proof You Needed to Start Investing and Saving Yesterday

I was working with some calculations the other day and something became ridiculously apparent to me.  You and I (along with almost anyone) literally can’t afford to wait to start investing and savings.

Calculating Contribution and Investing Returns

I think a very simple example will provide evidence that you need to start contributing, investing and saving yesterday.  

Person A vs. Person B

  • Both are 22 years old
  • Person A decided to contribute $2,000 for the first 10 years of his or her working life to any type of investment vehicle you can think of.  Person A inexplicably stops after the first 10 years.  Not sure why they would but its just an example.
  • Person B thinks that he is unable to afford the contributions and says I’ll wait.  He does wait but at the ripe age of 32 decides now is the time and invests that same $2,000/yr for the next 33 years.
  • They invest in the exact same stocks, bonds, mutual funds, etc and receive 6% after tax linear growth until retirement at 65.

So Person A put in $20,000 and Person B put in $66,000 – who will have more money?

Person A

Age BOY Balance Contribution Growth EOY Balance
22 $0 $2,000 $120 $2,120
23 $2,120 $2,000 $247 $4,367
24 $4,367 $2,000 $382 $6,749
25 $6,749 $2,000 $525 $9,274
26 $9,274 $2,000 $676 $11,951
27 $11,951 $2,000 $837 $14,788
28 $14,788 $2,000 $1,007 $17,795
29 $17,795 $2,000 $1,188 $20,983
30 $20,983 $2,000 $1,379 $24,362
31 $24,362 $2,000 $1,582 $27,943
32 $27,943 $2,000 $1,797 $31,740
33 $31,740 $0 $1,904 $33,644
34 $33,644 $0 $2,019 $35,663
35 $35,663 $0 $2,140 $37,803
36 $37,803 $0 $2,268 $40,071
37 $40,071 $0 $2,404 $42,475
38 $42,475 $0 $2,549 $45,024
39 $45,024 $0 $2,701 $47,725
40 $47,725 $0 $2,864 $50,589
41 $50,589 $0 $3,035 $53,624
42 $53,624 $0 $3,217 $56,841
43 $56,841 $0 $3,410 $60,252
44 $60,252 $0 $3,615 $63,867
45 $63,867 $0 $3,832 $67,699
46 $67,699 $0 $4,062 $71,761
47 $71,761 $0 $4,306 $76,066
48 $76,066 $0 $4,564 $80,630
49 $80,630 $0 $4,838 $85,468
50 $85,468 $0 $5,128 $90,596
51 $90,596 $0 $5,436 $96,032
52 $96,032 $0 $5,762 $101,794
53 $101,794 $0 $6,108 $107,902
54 $107,902 $0 $6,474 $114,376
55 $114,376 $0 $6,863 $121,238
56 $121,238 $0 $7,274 $128,513
57 $128,513 $0 $7,711 $136,223
58 $136,223 $0 $8,173 $144,397
59 $144,397 $0 $8,664 $153,061
60 $153,061 $0 $9,184 $162,244
61 $162,244 $0 $9,735 $171,979
62 $171,979 $0 $10,319 $182,298
63 $182,298 $0 $10,938 $193,236
64 $193,236 $0 $11,594 $204,830
65 $204,830 $0 $12,290 $217,120

 

Person B

Age BOY BALANCE Contribution Growth EOY Balance
22 $0 $0 $0 $0
23 $0 $0 $0 $0
24 $0 $0 $0 $0
25 $0 $0 $0 $0
26 $0 $0 $0 $0
27 $0 $0 $0 $0
28 $0 $0 $0 $0
29 $0 $0 $0 $0
30 $0 $0 $0 $0
31 $0 $0 $0 $0
32 $0 $0 $0 $0
33 $0 $2,000 $120 $2,120
34 $2,120 $2,000 $247 $4,367
35 $4,367 $2,000 $382 $6,749
36 $6,749 $2,000 $525 $9,274
37 $9,274 $2,000 $676 $11,951
38 $11,951 $2,000 $837 $14,788
39 $14,788 $2,000 $1,007 $17,795
40 $17,795 $2,000 $1,188 $20,983
41 $20,983 $2,000 $1,379 $24,362
42 $24,362 $2,000 $1,582 $27,943
43 $27,943 $2,000 $1,797 $31,740
44 $31,740 $2,000 $2,024 $35,764
45 $35,764 $2,000 $2,266 $40,030
46 $40,030 $2,000 $2,522 $44,552
47 $44,552 $2,000 $2,793 $49,345
48 $49,345 $2,000 $3,081 $54,426
49 $54,426 $2,000 $3,386 $59,811
50 $59,811 $2,000 $3,709 $65,520
51 $65,520 $2,000 $4,051 $71,571
52 $71,571 $2,000 $4,414 $77,985
53 $77,985 $2,000 $4,799 $84,785
54 $84,785 $2,000 $5,207 $91,992
55 $91,992 $2,000 $5,639 $99,631
56 $99,631 $2,000 $6,098 $107,729
57 $107,729 $2,000 $6,584 $116,313
58 $116,313 $2,000 $7,099 $125,412
59 $125,412 $2,000 $7,645 $135,056
60 $135,056 $2,000 $8,223 $145,280
61 $145,280 $2,000 $8,837 $156,116
62 $156,116 $2,000 $9,487 $167,603
63 $167,603 $2,000 $10,176 $179,780
64 $179,780 $2,000 $10,907 $192,686
65 $192,686 $2,000 $11,681 $206,368

 

Yup, Person A has a larger balance ($217k vs $206k).  It is easy to get into the details, and fall victim of paralysis by analysis, but one of the basic points of personal finance is that regardless of the synonym you want to use (investing, contributing, savings, etc.) it should have started yesterday.

6 Responses to Mathematical Proof You Needed to Start Investing and Saving Yesterday

  1. I couldn’t agree more Evan. The calculator I have freely available off my website has a “Compounding Calculator” as one feature.
    I just jumped my 401k up t more than double what it was (from 7% moved up to 16%). That hurts my pocket pretty bad, and now that I see how much it will change my paycheck – due to custom W-4 changes I made years ago – I have to run it through my budget to see the full effect.

  2. Scary right? I’m almost 50 due to late start… I was contributing only a tiny amount to my 401(k) and due to this very same math you mentioned – BIG CHANGE I too have jumped up my pay contributions at 15% will hit the max allowed contribution for the year.

    Hindsight is 20/20, so it’s hurt me but at least I’ve got the gimball pushed in the right direction now. I hope others read your article too. Thanks for the detailed numbers. Regards, TK

    • Timothy…better late then never! Remember just b/c you are maxed out on 401K contributions it doesn’t mean your savings/investing should end. Start a non-qualified (non-retirement) investment account, maybe look into an insurance product or two made for retirement purposes or just horde cash!

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