The Math That Explains Why Saving the First 100k Is So Tough

It took me 10 years to save my first 100k. And then it only took about a year to cross over 150k. It turns out, that’s pretty normal.

Compound interest is an amazing thing, but it sure starts out slow. You need time and lots of capital invested for it to work its magic.

Today I want to break down in detail the math that explains why saving your first 100k is so hard, but your net worth starts exploding after you hit that milestone.

Our Baseline: Investing With No Return

Without any return on your investment, how long it takes you to hit any milestone depends entirely on how much you save.

For this whole post, we’ll be using $10,000 a year as our annual savings. There’s nothing special about $10,000. It’s a nice round number. It’s also an aggressive yet achievable savings goal for someone making the median salary.

Here’s what saving $100k looks like with no returns:

Obviously, you don’t even need a chart for this one. $100k divided by $10k a year is 10 years. Your balance goes up linearly by 10 dollars a year.

A 7% Rate of Return Saves Just Two Years

Now let’s look at what would have happened if you had invested in some low cost index funds and earned a 7% rate of return per year (a purely hypothetical return):

Well, at least the graph is prettier. We now have two colors: Your cumulative contributions and your cumulative returns. If you’re especially perceptive, you’ll even notice that the green line is starting to bend slightly upward. A preview of things to come.

But you’ll also notice that the blue dominates the chart. Saving your first $100k with compound interest involves you doing 75% of the work and your returns contributing just 25%.

The end result is that it takes you eight years instead of 10 to cross the six-figure plateau.

Not bad, but not life-changing.

A 7% Rate of Return Contributes an Extra 50% After 10 Years

But our first example showed what happened over 10 years, so let’s give compound interest two more years to do its thing:

This is certainly a little more impressive. You’ve saved up $100k, but compound interest has helped out with close to an additional $50k. You have nearly 50% more than you would if you had just been stuffing your money under a matress.

Again, this is much better than the least example, but still not life changing.

Chances are after 10 difficult years of saving you’d be nearly as disappointed with a balance of $150k as you would with $100k. You’re a quarter of the way through a typical career, but a long way from bigger milestones like seven figures.

A 7% Rate of Return Over 40 Years is Insane

This is the first eye-catching chart of the bunch. After three straight graphs dominated by blue, here we have one dominated by green.

As time passes, your contributions continue to increase linearly, but your returns increase exponentially.

By the time you hot 40 years, you have more than $2 million saved up, but you yourself actually saved less than half a million ($400k to be exact). Now we’re in the realm of the incredible.

Using the 4% rule, (and assuming a sensible asset allocation) you could retire at this point and withdraw $85,443 a year to live off of.

The 4% Rule: How Much Money Do You Need to Never Work Again?

Cumulative Returns as a Percent of Your Total Balance

We’ve looked at the numbers visuually through charts, now let’s take a peek at the actual numbers through a table.

Here’s what is happening to your money by year:

Year	Cumulative Contributions	Cumulative Returns	Return/Balance
1	$10,000	$700	7%
2	$20,000	$2,149	10%
3	$30,000	$4,399	13%
4	$40,000	$7,507	16%
5	$50,000	$11,533	19%
6	$60,000	$16,540	22%
7	$70,000	$22,598	24%
8	$80,000	$29,780	27%
9	$90,000	$38,164	30%
10	$100,000	$47,836	32%
11	$110,000	$58,885	35%
12	$120,000	$71,406	37%
13	$130,000	$85,505	40%
14	$140,000	$101,290	42%
15	$150,000	$118,881	44%
16	$160,000	$138,402	46%
17	$170,000	$159,990	48%
18	$180,000	$183,790	51%
19	$190,000	$209,955	52%
20	$200,000	$238,652	54%
21	$210,000	$270,057	56%
22	$220,000	$304,361	58%
23	$230,000	$341,767	60%
24	$240,000	$382,490	61%
25	$250,000	$426,765	63%
26	$260,000	$474,838	65%
27	$270,000	$526,977	66%
28	$280,000	$583,465	68%
29	$290,000	$644,608	69%
30	$300,000	$710,730	70%
31	$310,000	$782,182	72%
32	$320,000	$859,334	73%
33	$330,000	$942,588	74%
34	$340,000	$1,032,369	75%
35	$350,000	$1,129,135	76%
36	$360,000	$1,233,374	77%
37	$370,000	$1,345,610	78%
38	$380,000	$1,466,403	79%
39	$390,000	$1,596,351	80%
40	$400,000	$1,736,096	81%

Starting at year 18, more than half of your portfolio balance has come from investment returns. Every year that passes by, the percent of your total balance provided by your returns goes up.

At the time you cross over the first $100k, your contributions make up over 70% of your balance. By the time you cross over $2 million they make up less than 20%.

Yearly Returns vs. Yearly Contributions

Here’s another useful table. This one breaks down the contributions vs. returns by year using the values for just that year instead of the cumulative total:

Year	Contributions	Returns
1	$10,000	$700
2	$10,000	$1,449
3	$10,000	$2,250
4	$10,000	$3,108
5	$10,000	$4,026
6	$10,000	$5,007
7	$10,000	$6,058
8	$10,000	$7,182
9	$10,000	$8,385
10	$10,000	$9,672
11	$10,000	$11,049
12	$10,000	$12,522
13	$10,000	$14,098
14	$10,000	$15,785
15	$10,000	$17,590
16	$10,000	$19,522
17	$10,000	$21,588
18	$10,000	$23,799
19	$10,000	$26,165
20	$10,000	$28,697
21	$10,000	$31,406
22	$10,000	$34,304
23	$10,000	$37,405
24	$10,000	$40,724
25	$10,000	$44,274
26	$10,000	$48,074
27	$10,000	$52,139
28	$10,000	$56,488
29	$10,000	$61,143
30	$10,000	$66,123
31	$10,000	$71,451
32	$10,000	$77,153
33	$10,000	$83,253
34	$10,000	$89,781
35	$10,000	$96,766
36	$10,000	$104,239
37	$10,000	$112,236
38	$10,000	$120,793
39	$10,000	$129,948
40	$10,000	$139,745

Year 11 is where this table turns. For the first 10 years, you’re doing the heavy lifting. Starting at year 11, your money starts contributing more than you do. And it never looks back.

By year 17 your money is working twice as hard as you are.

By year 21 it’s working three times as hard.

But both of those numbers are nothing. By year 36, your money is working 10 times as hard as you are.

Chances are in the later years your money might be making more money every year than you do.

The median household income is around $78k a year. If you’re making $78k and investing $10k at a 7% rate of return, your money starts out earning you in year 33.

Your Contributions Tend To Increase Over Time

We’ve really hit home the fact that compound interest takes time to work. The good news is that once it starts to work, it goes absolutely crazy.

But there’s another factor that makes the first 100k so hard to save. This is the fact that the beginning of your career is generally when you’re making the least.

I’m making way more per year and contributing way more per year than I was 10 years ago. I’ve given the example of saving $10,000 a year starting from year one, but that doesn’t look like real life. I was contributing way less than $10,000 a year in year one. I’m contributing more now. In the future, I’ll probably be contributing way more.

Let’s take a look at what it looks like to start out more slowly, but gain speed over time.

We’re going to use the same 7% return as before, but this time we’re going to start with a $7,000 contribution in year one and increase it by 3% per year:

It’s hard to tell because the green still dominates the chart, but now the blue line is curving upwards as well.

You might also notice that in our first example we had saved up $400k by the time it was all said and done. By starting slow but increasing our contributions along the way, we’ve ended up at a nearly identical $2.1 million, but we invested more than $500,000 along the way.

Here’s what our cumulative contributions vs. returns table looks like now:

Year	Cumulative Contributions	Cumulative Returns	Return/Balance
1	$7,000	$490	7%
2	$14,210	$1,519	10%
3	$21,636	$3,140	13%
4	$29,285	$5,410	16%
5	$37,164	$8,390	18%
6	$45,279	$12,147	21%
7	$53,637	$16,751	24%
8	$62,246	$22,281	26%
9	$71,114	$28,819	29%
10	$80,247	$36,454	31%
11	$89,655	$45,281	34%
12	$99,344	$55,405	36%
13	$109,325	$66,936	38%
14	$119,604	$79,994	40%
15	$130,192	$94,707	42%
16	$141,098	$111,213	44%
17	$152,331	$129,661	46%
18	$163,901	$150,211	48%
19	$175,818	$173,033	50%
20	$188,093	$198,311	51%
21	$200,735	$226,245	53%
22	$213,757	$257,045	55%
23	$227,170	$290,940	56%
24	$240,985	$328,175	58%
25	$255,215	$369,012	59%
26	$269,871	$413,734	61%
27	$284,967	$462,643	62%
28	$300,516	$516,064	63%
29	$316,532	$574,346	64%
30	$333,028	$637,862	66%
31	$350,019	$707,014	67%
32	$367,519	$782,231	68%
33	$385,545	$863,975	69%
34	$404,111	$952,741	70%
35	$423,235	$1,049,060	71%
36	$442,932	$1,153,499	72%
37	$463,220	$1,266,669	73%
38	$484,116	$1,389,224	74%
39	$505,640	$1,521,865	75%
40	$527,809	$1,665,342	76%

You’ll notice that when it’s all said and done, your contributions only represent 76% of your balance instead of 81% like before. This is because the early contributions matter more than later ones.

Let’s look at the non-cumulative chart:

Year	Contributions	Returns	Balance
1	$7,000	$490	$7,490
2	$7,210	$1,029	$15,729
3	$7,426	$1,621	$24,776
4	$7,649	$2,270	$34,695
5	$7,879	$2,980	$45,554
6	$8,115	$3,757	$57,425
7	$8,358	$4,605	$70,389
8	$8,609	$5,530	$84,528
9	$8,867	$6,538	$99,933
10	$9,133	$7,635	$116,701
11	$9,407	$8,828	$134,936
12	$9,690	$10,124	$154,749
13	$9,980	$11,531	$176,261
14	$10,280	$13,058	$199,598
15	$10,588	$14,713	$224,899
16	$10,906	$16,506	$252,311
17	$11,233	$18,448	$281,992
18	$11,570	$20,549	$314,112
19	$11,917	$22,822	$348,851
20	$12,275	$25,279	$386,404
21	$12,643	$27,933	$426,980
22	$13,022	$30,800	$470,802
23	$13,413	$33,895	$518,110
24	$13,815	$37,235	$569,160
25	$14,230	$40,837	$624,227
26	$14,656	$44,722	$683,605
27	$15,096	$48,909	$747,610
28	$15,549	$53,421	$816,581
29	$16,015	$58,282	$890,878
30	$16,496	$63,516	$970,890
31	$16,991	$69,152	$1,057,032
32	$17,501	$75,217	$1,149,750
33	$18,026	$81,744	$1,249,520
34	$18,566	$88,766	$1,356,852
35	$19,123	$96,318	$1,472,294
36	$19,697	$104,439	$1,596,431
37	$20,288	$113,170	$1,729,889
38	$20,897	$122,555	$1,873,340
39	$21,523	$132,640	$2,027,504
40	$22,169	$143,477	$2,193,151

I included the total this time because I wanted us to notice when we crossed over $100k. We came so close at the end of year nine but ultimately ended up crossing over early in year 10.

Remember, it took a full 10 years investing $10k a year with no returns. It took just eight years investing $10k a year with a 7% return. By starting out slow, it adds more than an additional year to your journey. That doesn’t sound like a lot in a blog post but it’s a lot in real life.

Final Thoughts

Compound interest needs time and capital to work. When you’re just getting started you have time ahead of you, but no time behind you. You also haven’t accumulated any meaningful capital. As you stay consistent, both of these variables grow together and the results are staggering.

The big idea is that early on, your returns are far less important than your contributions.

This means that the best thing you can do when it comes to investing is not to maximize your returns, but your contributions. Figure out how to spend less. Figure out how to earn more. And of course, invest the difference.

Getting your first 100k will be brutal. But it will get easier from there.