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The Magic of Compounding Interest

The Magic of Compounding Interest

The Magic of Compounding Interest

 It’s not at all a secret. It’s the world’s greatest invention as Albert Einstein puts it. But I’m not so sure if everybody makes good use of it. It’s compound interest, and though I know everybody knows that time is money, I’m not 100% confident to say that people actually save or invest to take advantage of this wonderful invention.

An Example

 Supposed I invest Php10,000 which earns 5% every year, how much money will I have in 10 years?

Year
Principal
Interest
Earned
Total
Year 1
   10,000.00
5%
         500.00
   10,500.00
Year 2
   10,500.00
5%
         525.00
   11,025.00
Year 3
   11,025.00
5%
         551.25
   11,576.25
Year 4
   11,576.25
5%
         578.81
   12,155.06
Year 5
   12,155.06
5%
         607.75
   12,762.82
Year 6
   12,762.82
5%
         638.14
   13,400.96
Year 7
   13,400.96
5%
         670.05
   14,071.00
Year 8
   14,071.00
5%
         703.55
   14,774.55
Year 9
   14,774.55
5%
         738.73
   15,513.28
Year 10
   15,513.28
5%
         775.66
   16,288.95

If it were just a simple interest formula, you might compute it this way:

Php10,000 x 5% x 10 = Php5,000 hence a sum of Php15,000.

But looking at the above table, your Php10,000 is actually Php16,288.95 in 10 years! Why is that so, because your interests earned every year also earn 5%. And summing them up together, you actually get a higher figure.

Let’s look at other tables with interest rates of 10%, 15% and 20%:

Year
Principal
Interest
Earned
Total
Year 1
   10,000.00
10%
     1,000.00
   11,000.00
Year 2
   11,000.00
10%
     1,100.00
   12,100.00
Year 3
   12,100.00
10%
     1,210.00
   13,310.00
Year 4
   13,310.00
10%
     1,331.00
   14,641.00
Year 5
   14,641.00
10%
     1,464.10
   16,105.10
Year 6
   16,105.10
10%
     1,610.51
   17,715.61
Year 7
   17,715.61
10%
     1,771.56
   19,487.17
Year 8
   19,487.17
10%
     1,948.72
   21,435.89
Year 9
   21,435.89
10%
     2,143.59
   23,579.48
Year 10
   23,579.48
10%
     2,357.95
   25,937.42
Year
Principal
Interest
Earned
Total
Year 1
   10,000.00
15%
     1,500.00
   11,500.00
Year 2
   11,500.00
15%
     1,725.00
   13,225.00
Year 3
   13,225.00
15%
     1,983.75
   15,208.75
Year 4
   15,208.75
15%
     2,281.31
   17,490.06
Year 5
   17,490.06
15%
     2,623.51
   20,113.57
Year 6
   20,113.57
15%
     3,017.04
   23,130.61
Year 7
   23,130.61
15%
     3,469.59
   26,600.20
Year 8
   26,600.20
15%
     3,990.03
   30,590.23
Year 9
   30,590.23
15%
     4,588.53
   35,178.76
Year 10
   35,178.76
15%
     5,276.81
   40,455.58

At 15% interest rate, your investment of Php10,000 has actually doubled at Year 5!

If you apply the Rule of 72, it’s a good estimate: 72 / 15 = 4.8

Year
Principal
Interest
Earned
Total
Year 1
   10,000.00
20%
     2,000.00
   12,000.00
Year 2
   12,000.00
20%
     2,400.00
   14,400.00
Year 3
   14,400.00
20%
     2,880.00
   17,280.00
Year 4
   17,280.00
20%
     3,456.00
   20,736.00
Year 5
   20,736.00
20%
     4,147.20
   24,883.20
Year 6
   24,883.20
20%
     4,976.64
   29,859.84
Year 7
   29,859.84
20%
     5,971.97
   35,831.81
Year 8
   35,831.81
20%
     7,166.36
   42,998.17
Year 9
   42,998.17
20%
     8,599.63
   51,597.80
Year 10
   51,597.80
20%
   10,319.56
   61,917.36

Your Php10,000 has gone six hundredfold in 10 years due to compound interest =)

For the geeky ones, this formula is:

F = P(1+i)^n

Where F = what we’re solving for – the future amount we will receive
P = present amount of the capital
I = interest rate
n = number of periods

In our case:

61,917.36 = 10,000(1+.20)^10

Google for nice online calculators so you don’t have to compute for this on your own.

Takeaways?

The earlier you start, the longer your money compounds. However, there could be investments with no guaranteed returns. Big things come from small things, hence, your Php10,000 invested years ago would have gained more if invested in a positively earning investment. Invest wisely!

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