Understanding How Compound Interest Works


I have been an educator for over thirty years as well as an investment and financial advisor. One of the mathematical concepts I love to teach students and families is how compounding interest works. I will start off with a penny, then ask my students how much would they have in a month if they took a penny, one cent, and doubled it each day? Usually they expect an over the top answer from me and so the answers can be anywhere from $20 to over a $100. Rarely would a student even get close unless they heard this notion before. When talking to families and comparing various Mutual and Index Funds, I would ask, would you rather have one million dollars or a penny to start with and then doubling it for a month? So, what do you get by doubling a penny a day for thirty-one days?

Day 1: $.01
Day 2: $.02  (01*02=.02)
Day 3: $.04  (02*02=.04)
Day 4: $.08  (04*02=.08)
Day 5: $.16  (08*02=.16)
Day 6: $.32
Day 7: $.64
Day 8: $1.28
Day 9: $2.56
Day 10: $5.12
Day 11: $10.24
Day 12: $20.48
Day 13: $40.96
Day 14: $81.92  (81.92 *02=163.84) Day 15: $163.84
Day 16: $327.68
Day 17: $655.36
Day 18: $1,310.72
Day 19: $2,621.44
Day 20: $5,242.88
Day 21: $10,485.76  ($5,242.88*02=$10,485.76)
Day 22: $20,971.52
Day 23: $41,943.04
Day 24: $83,886.08
Day 25: $167,772.16
Day 26: $335,544.32
Day 27: $671,088.64
Day 28: $1,342,177.28
Day 29: $2,684,354.56
Day 30: $5,368,709.12  (2,684,354.56*02=5,368,709.12)

This is an illustration on the power of compounding interest. The secret of getting rich slowly and safely. It can take some time, but after day 14 you can really see its power. The intent is to show how it works and where to best safely invest your money, so your money will work and grow for you and your family.


The Rule of 72, a logarithmic calculation, was perhaps discovered by Luca Pacioli, a renowned Italian mathematician, as he has the first reference of the Rule of 72 from his work in 1494, Summa de arithmetica, geometria, proportioni et proportionalita (“Summary of Arithmetic, Geometry, Proportions, and Proportionality”). It is alleged that Albert Einstein considered it one of the great math discovery’s along with his E=MC2 (Squared). Because when you invest money, you earn interest on your capital. This is determined by how long an investment will take to double given a fixed annual rate of interest by dividing the number 72 by the annual rate of return. Then, you can estimate how many years it will take for the initial investment to double.


In an investing scenario, such as a good stable Mutual or Index Fund you will earn interest on your money. Thus, that interest, then earns interest upon itself and the amount is compounded monthly. The higher the interest, the greater your money will grow!

Let’s look how this works in investing and retirement savings:

If you saved $100 each month, at 2% interest, after 30 years you would have $49,272.54. The amount from a good, stable high interest bank account (usually requires more than 500k in it.)

If you saved $100 each month, at 3% interest, after 30 years you would have $58,273.69. The amount from a good stable Credit Union.

If you saved $100 each month, at 5% interest, after 30 years you would have $83,225.86. The amount from a good stable Mutual Fund.

If you saved $100 each month, at 10% interest, after 30 years you would have $226,048.79. The amount from a risky high-end Mutual Fund if you do not lose it, it is not guaranteed).  Or, the amount from a low yield Index Fund where you will not lose your money. Actual investments will fluctuate in value, going higher or lower, but never below zero even in 1987 and 2008!

If you saved $100 each month, at 15% interest, after 30 years you would have $692,327.96. The amount from a risky high-end Stock Fund if you do not lose it, as it is not guaranteed).  Or, the amount from a high yield Index Fund where you will not lose your money.

Warren Buffett loves index Funds. He told CNBC’s Squawk Box on Feb 25, 2019, that if someone invested $10,000 in an index fund back in 1942, it would be worth $51 million today.

The power of compounding interest works even better when you increase your investment each month or year.

Why is compound interest so important?

Because your rate of return on interest will make a deposit or loan (rate of loss) grow at a faster pace than just simple interest. Thus, you will be earning a return not only on your original deposit, but also on the “accumulated interest” that you have gained on your past investment or retirement savings. Whereas, simple interest is interest calculated only on the principal amount.


Compound Interest

Now, what if you did more than $100 a month?

Find out here: https://investinganswers.com/calculators/saving/simple-savings-calculator-how-much-could-i-save-over-time-3679  or https://www.investor.gov/additional-resources/free-financial-planning-tools/compound-interest-calculator

The sooner you start to save, the greater your retirement savings will have by the power of compound interest.

Let me know how I can help you and put these in tax free retirement accounts that you can draw from if needed…

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