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Long term savings and compounding

There’s an old joke involving a mathematician and others on a deserted island which ends with the mathematician saying “Suppose you had a can opener.”, which of course they don’t and so it doesn’t solve the problem of opening their can of food.  Well this post is going to start with a mathematician stating “suppose you could get a constant 6% annual savings rate for 40 years” which of course you can’t.  The problem of long-term investing is a very complex problem and not just because you can’t get a constant unvarying return.  But let’s suppose you could get a constant rate of return and examine the effect of starting to save earlier rather than later and making a commitment to saving a life time goal.  

I do have three kids but I won’t use their names just to save them from embarrassment.  Let’s just say the first kid starts saving $100 a month when he’s 25 and continues saving until he reaches 65.  The second kid starts saving the same amount when she turns 25 but decides she needs the income when she’s 35 and stops saving.  Lastly the third kid doesn’t start saving until he’s 35 but he continues until he’s 65.   The question is how well will each of them have done by the time they reach 65?

The first one will have saved $48,000 over 40 years (40 years * 12 months * $100).  The second will have saved $12,000 over 40 years (10 years * 12 months *$100) and the third will have save $36,000 over 40 years (30 years * 12 months * $100).  But these different amounts of savings were accomplished over different lengths of time and different time periods resulting in differing amounts of cumulative growth.  The results are shown in the graph below.

The first kid’s savings have accumulated to roughly $200,000.  The second kid’s savings, the one who quit saving after 10 years, have grown but only to roughly $100,000.  Lastly, the third kid’s savings, the one who didn’t start saving until 35, have also grown to roughly $100,000.      


What are the takeaways from this chart?  The most obvious is that consistently saving over a longer period of time produces the best result.  Another obvious conclusion is that the second kid’s savings grew to a respectable amount over time even though it’s only half the first kid’s savings.  A less obvious realization is that the third kid had to save three times the amount the second kid saved and save it for thirty years, not just ten, to match the second kid’s savings at 65.  The least obvious realization is that the first kid’s savings plan is really just the combination of the second and third child’s savings plan, i.e. his first ten years of savings matches the savings of the second kid and his savings for the last thirty years matches the savings of the third kid.  Or to put it another way, half of his savings after 40 years came from his savings in the first ten years and half from his savings in the next thirty years.

Unique Circumstances:

Clearly everyone has their own unique situation where things happen in life which may disrupt a savings plan but there are several key aspects to consider in light of compound growth.  It is better to start saving consistently when you’re younger.  If something changes so you absolutely can’t keep saving you should, if at all possible, try to use current income instead of what you’ve already saved since that is what has the longest time to grow.  Lastly, it’s never too late to start saving but the longer you wait the more muted results will be just because you don’t have as much time for your savings to grow.  

In closing it must be said again that this example started by stating “suppose you could get a constant 6% annual savings rate for 40 years”.  This is a highly unrealistic assumption.  The long-term investment problem has a myriad of complexities and just one of them is that returns are rarely constant over the long run.  It is the concept of volatility which capturers this variability of returns and will be explored further in future posts.  Nevertheless, this hypothetical example does show the power and the limitations of long-term compound growth.

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Disclaimer:  The results in this post are all simplified hypothetical examples constructed merely to help understand the parameters of the mathematics surrounding the investment problem.  These are not actual investment returns that have occurred in any portfolio that Adaptive Financial Solutions has managed and they should not to be construed as returns that Adaptive Financial Solutions is advertising or claiming that it can produce.  Past results are no guarantee of future results and all of the information provided here should be discussed with an advisor, accountant or legal counsel prior to any attempt at implementation.