From Cents to Millions: Understanding the Compounding Effect

• What is coumpounding and how does it work? 

As a simple example, think about the median house in Sydney. In 1970, it was $18,700. Today, the fiture, post-Covid-19 is close to $1.6 million. In just over 50 years, it has increased by an eye-watering 7921 per cent. 

Compouding, by definition is earinig interest on interest.

• Let's test if you actually understood the compounding effect.

One day, if your employer offers either $1 million for working for them for 31 days, or to give you a cent a day and double it every day for 31 days, 

what would you choose?

1 cent becomes 2, becomes 4, becomes 8, becomes 16. On your 15th day, you will have only $327.67. However, it builds up exponentially.

If you choose the first option, you get $1,000,000.

However, if you choose the second option, you get $21,474,836.47.

Here I break it down:

Day	Money ($)
1	0.01
2	0.02
3	0.04
4	0.08
5	0.16
6	0.32
7	0.64
8	1.28
9	2.56
10	5.12
11	10.24
12	20.48
13	40.96
14	81.92
15	163.84
16	327.68
17	655.36
18	1,310.72
19	2,621.44
20	5,242.88
21	10,485.76
22	20,971.52
23	41,943.04
24	83,886.08
25	167,772.16
26	335,544.32
27	671,088.64
28	1,342,177.28
29	2,684,354.56
30	5,368,709.12
31	10,737,418.24
32	21,474,836.47

• What happen if I put $1000 earning 5 percent, and compoundng montly for 15 years?

We can use the compound interest formula:

$$A=P{(1+\frac{r}{n})}^{nt}A\; =\; P\; \backslash left(1\; +\; \backslash frac\{r\}\{n\}\backslash right)^\{nt\}$$

Where:

• $AA$ is the amount of money accumulated after $nn$ years, including interest.

• $PP$ is the principal amount (the initial amount of money, $1,000).

• $rr$ is the annual interest rate (5%, or 0.05).

• $nn$ is the number of times that interest is compounded per year (monthly, so 12).

• $tt$ is the number of years the money is invested (15 years).

Plugging in these values:

$$A=1000{(1+\frac{0.05}{12})}^{12\times 15}A\; =\; 1000\; \backslash left(1\; +\; \backslash frac\{0.05\}\{12\}\backslash right)^\{12\; \backslash times\; 15\}$$

$$\mathrm{<br>}A=1000{(1+0.004167)}^{180}A\; =\; 1000\; \backslash left(1\; +\; 0.004167\backslash right)^\{180\}$$

$$\mathrm{<br>}A=1000{\left(1.004167\right)}^{180}A\; =\; 1000\; \backslash left(1.004167\backslash right)^\{180\}$$

$$\mathrm{<br>}A\approx 1000\times 2.1137A\; \backslash approx\; 1000\; \backslash times\; 2.1137$$

$$\mathrm{<br>}A\approx 2113.70\mathrm{<span\; style="font-family:\; arial;"><br></span>}A\; \backslash approx\; 2113.70$$

So, after 15 years, your $1,000 investment would grow to approximately $2,113.70 with monthly compounding at an annual interest rate of 5%. 

If it was $100,000 then it would be $211,370.

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I understand $1,000 might seem small when the media and news are constantly highlighting how influencers make vast sums of money effortlessly.

However, it’s all about how small savings accumulate wealth over time.

For more information on how to make your money have a snowball effect, I highly recommend "The Richest Man in Babylon" by George S. Clason.

Hope you have a wonderful day💗