woes or fortunes - the power of compounding
Albert Einstein, one of the greatest thinkers of the 20th century, once quoted as saying that the greatest invention man has ever made is the idea of compound interest. Funny thing is, defining one single greatest invention is somewhat relative and relativity per se is what the geezer is famous of. Furthermore, relativity tackles at one point time as the center of this whole mind game. Compound interest, meanwhile, has time as one of its essential parameters.
I'm not gonna talk further about Einstein's relativity and paradoxes (I've got lots of stuffs going on my head, by the way, after watching Primer on my PC and Inception in the theatre). Let's talk about the other thing, probably one of the most important foundations of money making - compounding interest. No one even knows for sure if Einstein really has something to say about compounding (http://www.snopes.com/quotes/einstein/interest.asp). But everyone who fully understand how this gem works, would hardly disagree that this is one of the greatest tool to financial independence. If you already knew about these stuff, you may want to skip this part. There's nothing new here. Just some old idea retold just for the sake of telling (because I can).
The two sides of the equation
I've been exposed to compounding interest early on. The bad kind. My parents were a bunch of chronic debtors. They don't plan for the future. They don't plan for anything other that the present time. So when I started going to college, there was no fund to finance my education. We had an athritic jeepney servicing town and the meager earnings go to all our family needs. And it's most of the time, not enough. My brother later also go to college. The deficit widens extremely and there's nothing to pay off a debt than another debt. My mother would continuously talk about debt interest generating interests which in turn will generate interest of their own and so on and so forth.
How much I hated that idea. It was sad actually. The capital amount lent would eventually double or triple if the amortization is not paid in full. Think of the lost money which should have gone to savings instead of paying the compounded interest which should have not been there in the first place if we were only prompt enough paying our dues on time. There was a struggle on my parent's part and eventually on my own when I was able to get a decent job. I continued paying the bloated debt that actually started out as small. It took a toll on my own financial status. I wasn't able to save and I shrug off investing and financial planning altogether as a rich man's game I could never be able to play. I learned to understand the whole situation somehow though. It was a lesson. Learned the hard way, yes, but nevertheless a valuable lesson I would never forget.
Along those harrowing ordeal, there's always a realization of how it feels to be on the other side of the equation. It must be great if I was the one receiving the bloated interest instead of the other way around. The creditor gets to enjoy the power of interests compounding without much effort as long as the money remained lent and unpaid. This is exactly the idea of compounding in general. This is what the financial literatures meant by making money work for you (and not working for money). Time is an essential parameter. The more time you let go of your money, the more time it has to accumulate wealth through interests begetting interests. The logic is pretty straightforward actually. We almost knew the concept and we knew it's there. At times we don't care because for all of us who aren't so adept in money matters does not know how to exploit the power of compounding to our own advantage. This is the very reason why rich people say a peso can create millions someday.
Compounding simplified
Suppose you have a spare Php10,000 you wanted to put in an investment vehicle (e.g. lending company) that assures you of a 10% annual compounded rate of return. You were thinking of leaving this money there for 30 years. Within that period, how much your initial investment would accumulate? In how many years the initial investment will double? Triple? Quadruple?
A simple illustration would be very helpful. Initially, you had 10,000. Let's call this Year 0. After 1 year, this 10,000 will accumulate 1,000 (that's 10% of 10000).
By the second year, the initial investment will accumulate another 1000. The 1000 interest earned earlier will earn 100. So
Do you see the pattern? The initial investment will accumulate an interest. Then the interests will earn their own respective interests. And you'll see that your investment will grow slowly at first but interests earning interests will multiply and grow faster as the year goes by. On the contrary, you say you wanted to "earn" the interest - that is you wanted the company to pay you the 1,000 earned as dividends yearly. Who doesn't want a continuous cash flow right? But by receiving dividends equivalent to the earned interest, you doesn't let the interests to grow. That means, year after year, only the initial 10,000 is accumulating interest. Letting interest to compound gives back exponential growth in return. Without compounding, however, the growth is a boring linear.
You don't have to know exactly the mathematics behind exponential and linear graphs. It is safe to say, however, that linear growth gives you the same return throughout the years (a straight line). Exponential, on the other hand, gives much higher return if you let your investment untouched for a longer period. It is almost linear for the first few years but speeds up afterwards.
If you insisted continuing the manual computation above, you'll found out that your money will double in 8 years. Triple in 12th year. Quadruple in 15th year. By the end of 30th year, your 10,000 will accumulate a whopping Php174,494! That's 17x growth on your initial investment. The earlier you started, the longer your patience by letting your money accumulate somewhere, the higher the return.
Compounding applied.
Delinquent credit card payments applies the negative power of compounding. If you're one of those people who's stuck with paying only the minimum amount due monthly (which I was once), you might want to want to think very seriously of a plan to get out of that debt fast. Remember that compounding increases very fast if there are a lot of compoundings going on. In the case of credit cards, that's monthly compounding - 12 times a year. Trust me, I've been there, and it's horrible.
Now, at some point you wanted to put your money in a mutual fund (MF) or unit investment trust fund (UITF), or variable life insurance plan (VUL). These are all investment vehicles that pools money from several people and in return invest the pooled money in the stock market, bonds or money market. You wanted to know which fund is getting better return with the least resistance to market downturn. For MFs, you can check fund performance in http://www.icap.com.ph/factsfignavps.asp. It shows annualized compounded rate of return for 1, 3, and 5 years. If a fund maintains a consistent higher rate than the others, then it must be a good fund. You must learn to differentiate, however, from a 5-year annualized compounded rate against a 5-year cumulative rate. The former is the average rate annually for 5 years. The latter is the total rate for the 5-year period. The same can also be learned from fund performance of UITFs (http://www.uitf.com.ph) and VULs (you might want to visit company websites offering the products e.g. Sunlife, Philam Life, Manulife etc).
At this point, let us go back to one of our original questions. If I had some initial investment and I wanted to put it in a business that will eventually earn at an attactive annual rate. How much will be the resulting value if I leave it to accumulate for, say 30 years?
The following formula, then, can come in handy.
where P is the initial investment, r is the annualized compounding rate of return and n is the number of years.
Let's plug in some data to provide some example.
That's the same result we got above. Now try 30 years. That would give us something around 174,494!
Using the formula, you can actually project your future investment value. This very same idea drive some people to minimize buying things and focusing on savings and investment and doing business. This very same idea, gives you the assurance that your meager initial money will somehow grow (in our case, exponentially). You only need to scout for investments that gives you a favorable return. Don't forget to consider the risks involve, though. After you studied your investment strategy, with the power of compounding on your side, you'll never go wrong. The most important thing is that you never stop learning.
The power of compounding is actually very simple. At least for me, I see everything very differently. I'm not a fan of buying things anymore. Unlike before I frequented computer stores and gadget shops where things are not cheap. I save. Because I am not planning to work forever. We all can agree when the experts said, your money can work for you. And not the other way around. Try to remember the single important formula above. It might come in handy when you are faced with important financial decisions. And I know, some math is pretty exciting if it involves money your way, ain't it?
I'm not gonna talk further about Einstein's relativity and paradoxes (I've got lots of stuffs going on my head, by the way, after watching Primer on my PC and Inception in the theatre). Let's talk about the other thing, probably one of the most important foundations of money making - compounding interest. No one even knows for sure if Einstein really has something to say about compounding (http://www.snopes.com/quotes/einstein/interest.asp). But everyone who fully understand how this gem works, would hardly disagree that this is one of the greatest tool to financial independence. If you already knew about these stuff, you may want to skip this part. There's nothing new here. Just some old idea retold just for the sake of telling (because I can).
The two sides of the equation
I've been exposed to compounding interest early on. The bad kind. My parents were a bunch of chronic debtors. They don't plan for the future. They don't plan for anything other that the present time. So when I started going to college, there was no fund to finance my education. We had an athritic jeepney servicing town and the meager earnings go to all our family needs. And it's most of the time, not enough. My brother later also go to college. The deficit widens extremely and there's nothing to pay off a debt than another debt. My mother would continuously talk about debt interest generating interests which in turn will generate interest of their own and so on and so forth.
How much I hated that idea. It was sad actually. The capital amount lent would eventually double or triple if the amortization is not paid in full. Think of the lost money which should have gone to savings instead of paying the compounded interest which should have not been there in the first place if we were only prompt enough paying our dues on time. There was a struggle on my parent's part and eventually on my own when I was able to get a decent job. I continued paying the bloated debt that actually started out as small. It took a toll on my own financial status. I wasn't able to save and I shrug off investing and financial planning altogether as a rich man's game I could never be able to play. I learned to understand the whole situation somehow though. It was a lesson. Learned the hard way, yes, but nevertheless a valuable lesson I would never forget.
Along those harrowing ordeal, there's always a realization of how it feels to be on the other side of the equation. It must be great if I was the one receiving the bloated interest instead of the other way around. The creditor gets to enjoy the power of interests compounding without much effort as long as the money remained lent and unpaid. This is exactly the idea of compounding in general. This is what the financial literatures meant by making money work for you (and not working for money). Time is an essential parameter. The more time you let go of your money, the more time it has to accumulate wealth through interests begetting interests. The logic is pretty straightforward actually. We almost knew the concept and we knew it's there. At times we don't care because for all of us who aren't so adept in money matters does not know how to exploit the power of compounding to our own advantage. This is the very reason why rich people say a peso can create millions someday.
Compounding simplified
Suppose you have a spare Php10,000 you wanted to put in an investment vehicle (e.g. lending company) that assures you of a 10% annual compounded rate of return. You were thinking of leaving this money there for 30 years. Within that period, how much your initial investment would accumulate? In how many years the initial investment will double? Triple? Quadruple?
A simple illustration would be very helpful. Initially, you had 10,000. Let's call this Year 0. After 1 year, this 10,000 will accumulate 1,000 (that's 10% of 10000).
Year 1 amount = 10,000 + 1,000 = 11,000
By the second year, the initial investment will accumulate another 1000. The 1000 interest earned earlier will earn 100. So
Year 2 amount = (10,000 + 1,000) + (1,000 + 100)
= 12,100
Do you see the pattern? The initial investment will accumulate an interest. Then the interests will earn their own respective interests. And you'll see that your investment will grow slowly at first but interests earning interests will multiply and grow faster as the year goes by. On the contrary, you say you wanted to "earn" the interest - that is you wanted the company to pay you the 1,000 earned as dividends yearly. Who doesn't want a continuous cash flow right? But by receiving dividends equivalent to the earned interest, you doesn't let the interests to grow. That means, year after year, only the initial 10,000 is accumulating interest. Letting interest to compound gives back exponential growth in return. Without compounding, however, the growth is a boring linear.
 |
| click to maximize |
You don't have to know exactly the mathematics behind exponential and linear graphs. It is safe to say, however, that linear growth gives you the same return throughout the years (a straight line). Exponential, on the other hand, gives much higher return if you let your investment untouched for a longer period. It is almost linear for the first few years but speeds up afterwards.
If you insisted continuing the manual computation above, you'll found out that your money will double in 8 years. Triple in 12th year. Quadruple in 15th year. By the end of 30th year, your 10,000 will accumulate a whopping Php174,494! That's 17x growth on your initial investment. The earlier you started, the longer your patience by letting your money accumulate somewhere, the higher the return.
Compounding applied.
Delinquent credit card payments applies the negative power of compounding. If you're one of those people who's stuck with paying only the minimum amount due monthly (which I was once), you might want to want to think very seriously of a plan to get out of that debt fast. Remember that compounding increases very fast if there are a lot of compoundings going on. In the case of credit cards, that's monthly compounding - 12 times a year. Trust me, I've been there, and it's horrible.
Now, at some point you wanted to put your money in a mutual fund (MF) or unit investment trust fund (UITF), or variable life insurance plan (VUL). These are all investment vehicles that pools money from several people and in return invest the pooled money in the stock market, bonds or money market. You wanted to know which fund is getting better return with the least resistance to market downturn. For MFs, you can check fund performance in http://www.icap.com.ph/factsfignavps.asp. It shows annualized compounded rate of return for 1, 3, and 5 years. If a fund maintains a consistent higher rate than the others, then it must be a good fund. You must learn to differentiate, however, from a 5-year annualized compounded rate against a 5-year cumulative rate. The former is the average rate annually for 5 years. The latter is the total rate for the 5-year period. The same can also be learned from fund performance of UITFs (http://www.uitf.com.ph) and VULs (you might want to visit company websites offering the products e.g. Sunlife, Philam Life, Manulife etc).
At this point, let us go back to one of our original questions. If I had some initial investment and I wanted to put it in a business that will eventually earn at an attactive annual rate. How much will be the resulting value if I leave it to accumulate for, say 30 years?
The following formula, then, can come in handy.
F = P (1 + r)n |
Let's plug in some data to provide some example.
P = 10000, r = 10% = 0.1, n = 2 years
Then, F = 10000 (1 + 0.1)2
= 12,100
That's the same result we got above. Now try 30 years. That would give us something around 174,494!
Using the formula, you can actually project your future investment value. This very same idea drive some people to minimize buying things and focusing on savings and investment and doing business. This very same idea, gives you the assurance that your meager initial money will somehow grow (in our case, exponentially). You only need to scout for investments that gives you a favorable return. Don't forget to consider the risks involve, though. After you studied your investment strategy, with the power of compounding on your side, you'll never go wrong. The most important thing is that you never stop learning.
The power of compounding is actually very simple. At least for me, I see everything very differently. I'm not a fan of buying things anymore. Unlike before I frequented computer stores and gadget shops where things are not cheap. I save. Because I am not planning to work forever. We all can agree when the experts said, your money can work for you. And not the other way around. Try to remember the single important formula above. It might come in handy when you are faced with important financial decisions. And I know, some math is pretty exciting if it involves money your way, ain't it?
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