Money & Doctors: The Magic of Compounding


“Compound interest is the 8th Wonder of the World.”

-Albert Einstein

Numbers don’t lie.   Of any real truths in the world, this is one of them.  There is beauty in the simplicity of numbers.  Mix in a few letters, some Greek symbols, and extraordinary, almost magical formulas are begotten using those simple ten numerals from 0 to 9.

One of these amazing concepts is exponential growth.  Where money is concerned, exponential growth in the form of compounding interest is the path to outrageous fortune.  Unfortunately many folks, not just doctors, fail to realize the enormous value of regular saving and the power of compounding.

Exponential growth is a natural phenomenon, existing in the real world outside the realm of human invention.  Think of bacteria multiplying, starting from a single organism.  A bacterium reproduces by splitting itself into two.  One bacterium becomes two, then each of these divides to become 4, then 4 divide to become 8, and on and on until you get billions of those litter critters spreading in the petri dish, or God forbid, throughout your body.  The way math people describe this is y=xn where n is the number of times the base x is multiplied and y is the final result.  So if n = 8 and x =2, the result is 2x2x2x2x2x2x2x2 which equals 256. 

Imagine each bacterium represents a one-hundred-dollar bill.  You invest that $100 so that it doubles every year.  The formula y=100x28 would result in $25,600 in 8 years.

Of course, it would be wonderful to find an investment that doubles every year (which is the same as saying it yields a 100 percent annual return) or convert multiplying-bacteria into dollar bills.  No doubt you’ve been taught that money doesn’t grow on trees, nor on petri dishes.  But this example illustrates the tremendous power of compounding.  Only you can create exponential growth when It comes to your hard-earned money by saving and investing regularly.


Formulas for Calculating the Effects of Compounding Interest

A simple formula to calculate growth from compound interest on an investment:

A = P x (1 + i)n

Where P = principal (initial amount investment), i = interest rate per year (or rate of return), n = number of years investment is earning the interest, and A = future amount at the end of n year.

Suppose you invest $5,000 with an interest rate 8% a year compounding annually, and you invest it for 9 years.  What is the final amount after nine years?  Well, just plug in the numbers and we shall see:

                                                A = P x (1 + i)n

A = 5000 x (1 + 0.08)9 

     = 5000 x (1.08)9

    = 5000 x (1.9999)

    = 9,995

The result is $9,995 after 9 years, nearly a doubling of the final amount (A) after nine years.

However, interest often Is compounded more than once a year.  The formula then becomes:

A = P x (1 + r/m)mt

Where P and A are the same as in the prior formula, but r = interest rate per year, m = number of interest periods per year, and t = number of years.

So taking that same $5,000 investment at the same interest rate of 8% per year, but compounded monthly (meaning the interest in that month is then added to the principal P), the result is:

                                                A = 5000 x (1 + .08/12)12x9 = 5000 x (1 + 0.0067)108

                                                A = 5000 x 2.057 = 10,284

Thus, considerably more money is earned when there are more compounding periods in a year.


The Rule of 72

Instead of using the above formulas (or formulae in scientific jargon), you might find yourself reviewing financial information and need to quickly assess the value of a prospect in your head.  Often, you’ll find the need to think in terms of doubling one thing or another.  Financial folks use nifty terms such as “100% ROI (return on investment) in X amount of time,” meaning it will take X amount of years to make back your initial investment, or in other words, double your dough.  In essence, you’ll find yourself in situations where you want to double some number.  On the flip side, you might need to ascertain the rate of return required to double your investment over a given number of years.  There is a simple method called the Rule of 72.

The Rule of 72 is calculates a future value of an investment knowing the expected rate of return (i.e., the interest rate).  Vice versa, the rule is also used to calculate a rate of return based on the expected future value of an investment over a given number of years.  It’s a marvelous little tool that’s quite powerful in its concept; one can quickly churn out numbers impressively, fooling folks into believing you’re a super-genius on the same scale as Albert Einstein.  However, this only is useful for once-a-year compounding.  Here it is:

N = 72/i

where N = number of years to double the initial investment, i = annual interest rate.

Doing a little algebra, one can calculate the interest rate:

i = 72/N 

Suppose you have an investment earning 7% a year, this produces a value of:

N = 72/i

N = 72/7 = 10.3 years

In other words, it takes a little over 10 years to double your money if it’s earning 7% a year.  You can play with this, and you’ll find 8% doubles your investment in 9 years, 10% doubles it in 7 years.  Of course, these are rough estimates but are very helpful for on-the-fly determinations.

You can estimate a rate of return on an investment in the same way.  Let’s say you’d like your money to double every 6 years:

I = 72/N

i = 72/6 = 14.4 

Hence, you’d need an investment providing a rate of return (or interest rate) of roughly 12% over six years.


The Power of Compounding

Following are some examples showing the power of the exponential growth of compounding.

Let’s say a young very hard-working guy, whose not a doctor, can begin saving earlier, starting 25 years of age.  He puts away $100 a month.  He invests this money with an average rate of return of 7% per year.  The formula for compounding while making regular contributions is much more complicated than formulae mentioned before.  I won’t get into the complicated math, but the result is graphically demonstrated as follows in Figure 1.

Figure 1

In other words, when he retires at 65 years-old, he’ll have amassed over $262,000, with a total investment of $48,000.  That’s nearly a 5.5X increase (450%) on his total investment (his principal or total amount of money he put into his investments). 

To view this example another way, the data that formed the graph is found in the table below: 


Also shown in the table are other scenarios.  For instance, the next person is a doctor (Doctor A) who decides to start saving $250 per month, but starts later at 35 years of age.  She has a bit of catching-up to do.  Even though she’s stocking away more money per month, she only accumulates $305,000 by 65 years of age, taking $88,000 of principal to do so, resulting in a 3.5X increase on her total investment.  Compare this to the first guy, who invested less and had a much higher growth (5.5-fold) on his investment.

The next doctor (B) starts saving at 30 years-old and puts away the same $250 per month.  Starting just 5 years earlier results in $450,000 at 65 years, a 4.3X increase of his total investment.  He has $144,000 more than his colleague mentioned before, while investing only $16,500 more.

Figure 2 below demonstrates this graphically.  The difference between Doctor A and B is amazing.

Let's return to the table.  What happens if your rate of return increases?  Let’s say another doctor starts saving the same amount at the same age as he 30 year-old colleague.  However, she is able to invest at a 8% rate of return.  From the table, you can see her piggy bank is stuffed with over $573,000 at 65 years, yielding nearly 5.5X increase on her total investment.

Now see what happens when you delay your retirement by just one year.  In every example, the additional amount of money accumulated from 65 to 66 years is enormous, far exceeding the amount invested for that additional year.  So you can either retire a year later or start saving a year earlier.  Either way produces a huge difference in your accumulated wealth.

Below is the graph comparing the two doctors examples:

Figure 2

Hopefully, all of these folks should’ve increased their monthly savings during the course of their careers as their earnings increased.  The final numbers would thus be far, far greater.

These examples show the tremendous power of compounding over the long term.  The take-home message is start saving as early as you can.   Even one extra year makes an enormous (logarithmic) difference in your end-result.  Don’t put it off thinking you will easily catch up later; otherwise you’ll find yourself needing to sock away a whole lot more in the process, and may still be behind

During our schooling and training as doctors, we somehow avoided the topic of money, or at least in a sense of how it relates to ourselves.  Talk of money is taboo.  We were put on earth to save lives, heal the sick and not concern ourselves with ourselves.  Heck, we’re supposedly the symbols of ultimate altruism.  But we’re also human.

No one will take care of you when you retire, or in the unfortunate event you’re disabled and incapable of providing for yourself and your family.  This is THE reason, the big-time motivator to start saving early and regularly.  You can do it. 

We’ll talk more about investing strategies in future posts.

©Randall S. Fong, M.D.


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