One Mathematical Equation Simplifies A Law of the Universe

I attended The Feast one Sunday morning at PICC, Manila.  I've been to several sessions last year and this one particular Sunday was my first for this new year. True to what they're saying, The Feast is the happiest place on earth.  And I've got another happy place...It's anywhere as long as I'm with my son.  I think my son has superpowers.  He can turn any place, any day into a happy happy fun day, like magic!

At The Feast, Bo Sanchez once again delivered the most life-changing lessons, the Law of Compounding. He says that compounding is the hidden force behind all successes.  He told us a story and it goes something like this...My memory is short so apologies If I used, changed or  mixed-matched some names or places here.

Anyway, again, here is the story.

Henry got interviewed by the President of ABC Company, a large store, for a Supervisor position. Henry believed he got all the qualifications for the position and was confident he was going to be hired.  The president explained some more information about the position and the company and that the contract was for 36 months.  Henry was ecstatic and really liked the way the interview was going.  Some time during the discussion, Henry asked about the salary.  The president looked at him for a little while and then said that he had two options of paying of which Henry would choose.  The first option was to pay Henry would be paid 30,000 Php every month for 36 months. Henry liked this option and was very happy that he almost forgot there was another option. Feeling curious, Henry asked what the second option was.   The president said he would pay Henry 1 centavo for the first month but will double it the next month and will double again the doubled salary for the next month salary, and so on up until the end of the contract at 36th month. The president looked again at Henry and asked which one would Henry choose.   Not batting an eyelash, Henry chose 30,000 per month, even thanking the president for being that generous.  Right there after that, The president told Henry that he would not be getting the job.   Henry was shocked and asked why.  The president explained that Henry did not have a good decision-making skill.   He asked Henry to compute what he would have gotten after 36 months if he opted for the second choice which Henry bothered to compute but only got up to 12 months when he saw that the total was 20.48 pesos only. He said that it was just a waste of time to compute since he said he knew it would just sum up to a small amount while receiving 30,000 pesos per month would make him a millionaire after the contract.

Lesson? Always bring a calculator. Henry must have lost his somewhere, poor guy.

OK the real lesson is compounding.  Bo Sanchez says that compounding is the hidden force behind all successes.

Albert Einstein believed that compounding is the most powerful force in the universe.

What did Henry miss? He missed to recall his past lessons in algebra or maybe he skipped this class because he didn't really like it.  Here's the calculation, the long way, of Henry's income if he chose the second option.

n	r	amount to be doubled per month	an	Henry's Salary
1		0.01	0.01	1st month salary
2	2	0.01	0.02	2nd month salary
3	2	0.02	0.04	3rd month salary
4	2	0.04	0.08	4th month salary
5	2	0.08	0.16	5th month salary
6	2	0.16	0.32	6th month salary
7	2	0.32	0.64	7th month salary
8	2	0.64	1.28	8th month salary
9	2	1.28	2.56	9th month salary
10	2	2.56	5.12	10th month salary
11	2	5.12	10.24	11th month salary
12	2	10.24	20.48	12th month salary
13	2	20.48	40.96	13th month salary
14	2	40.96	81.92	14th month salary
15	2	81.92	163.84	15th month salary
16	2	163.84	327.68	16th month salary
17	2	327.68	655.36	17th month salary
18	2	655.36	1,310.72	18th month salary
19	2	1,310.72	2,621.44	19th month salary
20	2	2,621.44	5,242.88	20th month salary
21	2	5,242.88	10,485.76	21st month salary
22	2	10,485.76	20,971.52	22nd month salary
23	2	20,971.52	41,943.04	23rd month salary
24	2	41,943.04	83,886.08	24th month salary
25	2	83,886.08	167,772.16	25th month salary
26	2	167,772.16	335,544.32	26th month salary
27	2	335,544.32	671,088.64	27th month salary
28	2	671,088.64	1,342,177.28	28th month salary
29	2	1,342,177.28	2,684,354.56	29th month salary
30	2	2,684,354.56	5,368,709.12	30th month salary
31	2	5,368,709.12	10,737,418.24	31st month salary
32	2	10,737,418.24	21,474,836.48	32nd month salary
33	2	21,474,836.48	42,949,672.96	33rd month salary
34	2	42,949,672.96	85,899,345.92	34th month salary
35	2	85,899,345.92	171,798,691.84	35th month salary
36	2	171,798,691.84	343,597,383.68	36th month salary
Total Earnings			687,194,767.4	total salary received

where:
n	=	number of terms or months for this example
r	=	common ratio or when you double, triple, etc.

   an                  =              the nth term or Henry's salary for each month

 Henry would have been a very very very rich guy after 36 months with total earnings at 687 Million pesos!

The one above is from the spreadsheet calculation.  And the good thing is there is a short way to calculating it,  the Sum of the geometric progression!

This is so when r < 1.

This is when r > 1.

where:
S               =                  the sum of the geometric progression (in our example, this is the total earning)
a1                    =                  the first term (in our example is the 1 centavo or .01 Php)

I never knew that there is a Law of Compounding.  Nobody taught me this at school. I was only taught Algebra and the rest of math subjects, engineering so you know, nothing I could do about it.  Anyway, it's just so beautiful to realize that this simple equation can make people successful and rich once really applied. Heck, I can start planning my life now with start date of now and December 2022 as finish date and then cost load it using compounding. How much will I be getting after 2022? Goodness!

Francis Bacon is right, knowledge is power.