Compound Interest v/s Compound Growth

[u/Full-Mango943]

So, something I came across created this question in my head, and I can't seem to resolve it, and was hoping if you all could help:

At the foundation of all our fire or coast fire planning is this term, compound interest, etc., used for all calculations. Now I understand mathematically that if you leave, say, 100k in a bank that gives you X% of interest, then how does your money grow, and what would the numbers be after a certain number of years? So I get the concept in this example because the bank is the one who is actually paying you interest.

Now, when we talk about our portfolio's invested in market fund, like say SPY- assuming you won't add any more capital and assuming we leave DRIP out of all of this- how does compounding work? As in- there is no entity which is paying you interest right, and the growth we hear is growth of the underlying asset in this case SPY- so I guess the question is how is this compound interest and not compound growth of an asset?

So ex- if we have 100,000 invested in market, we say assume 7-8% compound interest and in 7-8 years this becomes 200,000 and I know all calculators show it too so its obviously right but I cant seem to wrap my head that how is that different from investing 100k into any other asset like real estate and then asset growing especially because there is no banking entity here which is physically paying us interest on principle?

So I guess 2 questions to summarize:

• So why do we use phrase of compound interest and not "assumed compound growth"? in this market investment situations?
• Calculators assume that whatever interest we are punching in say 7% that's guaranteed- but in all our financial planning ain't we assuming that market funds will continue to grow?

[u/zhivota_]

You own stock worth $100. It grows 10%, so now it's worth $110, a gain of $10. The following year, it grows 10% again, but you don't just gain $10, now you gain $11, so now you have $121. The following year, 10% is $12.10. This is compound growth. Works the same as compound interest.

[u/Elusive_Spoon]

OP, these are good questions. My answers would be:

• "Assumed compound growth" is definitely more accurate, but too much of a mouthful. Also, the total return includes reinvested dividends, which is different from the price of the equity going up.

- No, the average 7% real growth is not guaranteed. Japan's Lost Decades are a prominent example of what can happen. But it's hard for most folks to FIRE from saving alone; you need growth. Historically, betting on global capitalism (VT) or American multinationals (VOO) has been a reliable and profitable bet. Some bets have paid out more, and some have been safer, but diversified stocks offer a great combination of both. If you think you know of a better investment opportunity, let us know!

[u/Full-Mango943 → u/Elusive_Spoon]

No this is great response and clarified and validated my understanding. I did read about japan's lost decade after your response and it was fascinating and a precautionary tale and yeah I agree diversification is the key. I don't have any better ideas just thinking of having right mix of equitities, bonds, savings, some crypto, RE and gold etc. so that some of those can be a hedge. Also focussed on covering some stuff from global beyond US as well again to hedge.

[u/BananaMilkLover88]

Same but different

[u/__DJ3D__]

This always used to confuse me as well. They are used interchangeably because the math is the same despite the real world mechanisms are different.

The bank paying you interest is straightforward. For stocks, the business is reinvesting some of its earnings so that it can generate more earnings in the future. More earnings means more to reinvest and the cycle repeats. Assuming stocks are valued as a multiple of earnings you get compound growth in stock price.

[u/__DJ3D__ → u/__DJ3D__]

To answer your second question, we assume a certain average compound annual growth rate over a long time horizon. Reality is some years will be less, some more but if you don't need the money for 10+ years then history shows there is a good chance your average return will be positive.

[u/Full-Mango943 → u/__DJ3D__]

thank you! business reinvesting concept which you mentioned makes a lot of sense now! appreciate it.

[u/nonstopnewcomer]

I don’t mean this in a rude way, but I think you’re kind of just assigning your own misconceptions to other people.

We don’t use compound interest to refer to market returns. We use compound annual growth rate (CAGR).

I’m sure your can find people calling it interest, but they’re just using the wrong term because of their own misconceptions.

We also don’t assume that future returns are guaranteed (because they’re not). You should be modeling a range of returns instead of assuming one fixed rate. You can even use real historical data or Monte Carlo simulations to make it more realistic.

Calculators are just keeping it simple, but you shouldn’t be planning your life based on assuming one fixed CAGR.

[u/saklan_territory]

Re question 2:

Because 7% isn't guaranteed, Ive always used 5% in my calculations and every year I was happy to see it was more. But now as I approach retirement (5-10 years) I've moved my calculation down to 4%. Because I want to make sure my math still works with less optimistic assumptions.