# 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. Your math, as well as countless luminaries, have shown that time is your friend when it comes to compound interest.

• Evan says:

Now to convince the world! or don’t b/c it isn’t my problem lol

2. 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.

• Evan says:

I am confused…did you just double your contributions or realized you have to?

3. Timothy Kukler says:

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

• Evan says:

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!