Making Linux Work on Your PC, Part 1: Installing Linux Mint

Around a year ago, I replaced my aging Asus EEE PC with a Lenovo X230 Thinkpad that I got on a significant student discount. The X230 came with Intel's i5 processor, 8GB of ram, and Windows 7 Home Edition. My early experience with the system had been fairly pleasant, but soon the OS started to not work properly too frequently (I had to do a fresh install five times in the last six months) that I decided that the only long-term solution to my problem would be to shift to Linux: it's free, more stable, and current versions supposedly offer a user experience that rivals Mac OS's.

Linux Mint

Linux today is leap-years ahead of what we had a decade ago. Current incarnations of the OS from projects like Ubuntu are arguably just a couple of steps away from 100% mainstream usability, and initiatives like Linux Mint take things a step further by including important components such as audio and video codecs and useful software out of the box.

To install Linux Mint on your PC, start by looking at the Linux Mint community's hardware database to find out which version is most compatible with your system. For the X230, Linux Mint 14, code-named "Nadia," seems to be the best choice.

Linux Mint comes with different desktop environments that have been developed by independent groups over the years. I've heard good things about the "Cinammon" desktop, so I decided to use it. Once you have decided which flavor of Linux you want to use, download the DVD iso of the installer and burn the file into a DVD installer disk.

You have several alternatives in installing Linux Mint. One is to install it from within Windows as an application (mint4win). To do this, run the DVD while on Windows and install the OS as you would any other Windows software. While this option is more flexible since it's easy to uninstall if you change your mind, you only get to allocate a maximum of 30 GB of hard disk space to Linux.

Another option is to boot from the DVD and install the OS either side-by-side with Windows or to completely assign your hard drive to Linux. Both of these options offer greater hard drive space options and reportedly faster boot and run times. To maintain access to Windows (in case I need it for whatever reason), I decided to install Linux Mint as a second OS.

Fixing the sound bug

One frustrating bug in Nadia is the seeming lack of playback sound after installation. Fortunately, the fix (which comes from the Linux Mint forums) turns out to be quite easy.

1. First, open Menu > Software Manager. 
2. Type "alsa" in the search box and make sure that the packages "alsa-base," "alsa-utils," and "alsamixergui:i386" are installed. In my case, I had to install "alsamixergui:i386"
3. Run "alsamixer" in the terminal. A user interface with colored columns should appear.
4. Press the right directional key until it takes you to the "Auto-Mute Mode" column, which you should find "Enabled" (this is the cause of the issue). Press up or down to change the value to "Disabled."
5. Issue fixed. Close the terminal window.

Games, productivity, and other things

At this point, you should be able to use and enjoy your new Linux PC reasonably as it comes with everything you need for communication (the Firefox browser and the Thunderbird email client), productivity (Libre Office suite), and entertainment (VLC video player and the Banshee audio player, with all the codecs that you need). Still, the main reason why most people stick with Windows despite the advantages of Linux, particularly Linux Mint, in terms of price, stability, and more and more, usability, is the lack of games and other software. In Part 2, I'll show that this is not the case anymore, and that today there are very few reasons to stay with Windows.

Google Tips and Tricks for Students

I'm scrambling to beat my monthly quota, so I guess it's time for another lazy post.

I got this from Reddit.

Saving and Investing for Your Child's College Education

DEAR INVESTOR JUAN

Dear Investor Juan,

Please don't laugh at my silly question but is it possible to invest 10,000 pesos on something (don't know what kind of investment - UTIF maybe). Long term, maybe 15 years long. would my 10 000 earn enough that it can send my son to college?? It is his birthday next week and I just kept on thinking about his future.

Thanks. 

Nice blog by the way. i just stumbled it today and i kept reading about stocks and investments!

Joriel


Dear Joriel,

It's not a silly question, there's no need to apologize.

Assuming that inflation would be 5% per year and diversified equity funds (such as equity UITFs) will grow at an average rate of 10% per year for 15 years, then the real rate of return of investing in equity funds is 5% per year (please see this post for some background on real rates of return). 10,000 compounded by 5% per year for 15 years is

10,000*(1.05)^15 = 20,789 pesos

At today's prices, would this amount be enough for your son's college tuition? (It's more than enough for some colleges and universities, actually).

If you want to send your son to a university which currently charges 150,000 pesos per year for tuition so that in 15 years you want to have 600,000 in today's peso, then you have to invest this much today:

600,000/(1.05)^15 = 288,610 pesos

If you want to invest in annual installments, you can use the PMT function in Excel using the arguments:

rate = 5%

nper = 15

FV = 600,000

And you'll get 27,805 pesos (please ignore that the answer in Excel is negative), the amount that you have to invest every year (before adjusting for inflation) to have 600,000 in 15 years, assuming that the annual real rate of return is 5%. It's perfectly doable if you ask me. :)

I hope I was able to help. Good luck!

Almost-Forgotten Emails (Part 2)

DEAR INVESTOR JUAN

As I was trying to reduce the number of unread emails in my inbox, I discovered a handful of emails from almost half a year ago. Here's my attempt to make up and apologize for the oversight.

***

Dear Investor Juan,

Helpful po talaga yung blog mo. Mejo nagiisip isip po ako ngayon. Kasi ang balak ko po is to invest or purchase ng units every month sa bpi equity ko, im planning 2k-4k per month. And Im planning to do it for a long time. Tapos I have a friend na gusto mg invest sa individual stocks, yung kuya nya kasi ganun yung gngwa. Citisec po yung broker nla and I saw there EIP na 5k ang starting investment then pwd rn mgaadd anytime na gusto mo. Im thinking of investing din sa individual stocks kng san alam ko n tatagal and lalaki p yung company. 

My question is, kung papasok ako sa individual stocks, baba po yung ilalagay ko sa equities ko, and sabay ko po silang lalagyan ng pera monthly ? Should I just focus on equities or I can also try individual stocks? And do you have feedback about Citiseconline? 

Thank you IJ. 

Rek
February 6, 2013


Dear Rek,

Stick to the equity fund. Investing in individual stocks is too risky. There's not fool-proof way to pick stocks that will consistently outperform the market index or diversified equity funds. Also, by investing in individual stocks, you subject yourself needlessly to unique risk, which I have discussed in this post.

Finally, try to convince your friend to move to an equity fund, if it's not too late already.

***

dear investor juan,

good evening sir.
i've been reading your blogs a lot since i stumbled into it last week. i love your blog! it's been a great help.
from reading your blogs, i was already decided this morning on investing 1M on bdo equity funds.
but when i asked for an opinion from a metrobank investment officer about investing in equity funds now,she said it's better if i wait for the market correction. and it's too expensive now.
when i checked bloomberg.com just now,it increased by 1.27%.
what is your take on this sir?
i'd love to hear from you.
thank you.

kristina

February 18, 2013

Dear Kristina,

Well, in hindsight, the investment officer that you talked to appears to be a genius since the correction that he mentioned seem to have happened just recently.

It's kinda funny that so-called experts have a knack of saying that a correction will happen, but fall short of saying exactly when it will happen and by how much prices will go down.

Anyway, with regard to investing in the long term, short term fluctuations--"corrections" included--does not really matter. And if you can't afford a long-term horizon, I suggest investing in something safer like bond or money market funds.

***

Dear Investor Juan,

I have bdo and metro uitf and would like to know if it is a good time to invest with pnb-allied uitf. Pnb-allied uitf performed well for 2012 and I was thinking of bdo-equitable/pci merger,  now the bdo equity fund which I believe was originally equitable-pci product is performing way ahead of bpi or metro equity fund. So my question is in such mergers, does the uitf become better, what do you think of pnb-allied merger in particular will it be good time to invest in its uitf? Though I have exsisting accounts with both banks, the bank personnels/manager is not much help when I inquire saying the merger has just taken effect (feb 9) so no info is given to them.

Thanks,

Maxine

February 19, 2013

Dear Maxine,

I don't have data to support this claim, but I strongly believe that events such as bank mergers have nothing to do with the performance of UITFs. 

The performance of a fund depends on the performance of its constituent assets, and the composition of the fund (of a particular type) is determined by the fund manager. However, US data shows that skill may not be enough to consistently beat the market index. Finally, high fees make it even more difficult for investors to earn market-beating returns. IMO, neither of these factors--the skill of the fund manager and the level of fees--has anything to do with bank mergers.

Almost-Forgotten Emails (Part 1)

DEAR INVESTOR JUAN

As I was trying to reduce the number of unread emails in my inbox, I discovered a handful of emails from almost half a year ago. Here's my attempt to make up and apologize for the oversight.

***

Dear Investor Juan,

I have been visiting your blog for the past few months or so.

I had just cleared all my debts I have incurred while I was in college and my not so fortunate first job.

I was just starting to build up some savings when I stumbled upon your blog.

It was very reassuring knowing I was on the right track while reading your "A Guide for Newbie Investors" posts!

Thank you very much for sharing the things that you know.

I'm slowly trying to read backwards from your oldest post to the most recent ones, I'm even reading the comments!

Currently I am debt free and about 80% on my emergency fund.

As I have yet to actually venture into investing I am still a green horn so to speak and can only hope that you would indulged me and my questions.

• Do you still think UITF's are good vehicles for long term investments? (Already asked on older posts, just checking to see if it still is the case now)
• On the "A Guide for Newbie Investors", its says the next step for me would be to invest in assets with relatively lower risk, I did some checking comparing different funds, and it seems BDO outperforms its competitors every time (at least on the dates I've checked, as far as 2008 and even recent histories). Logically I would choose to invest on BDO, but seeing that their unit price for their balanced fund is currently valued at 3400~. It seems a bit steep and has a high chance that I would lose money even if I intend to invest on a long term basis. Am I wrong?
• Secondly, why is it that BDO balanced fund is valued so high compared to the other balanced funds and yet they still managed to out perform their competitors?   
• This is a silly, please humor me. Should the bank go under, would I still be able to claim my investments?
• Let's say I invested some money at 1000 pesos per unit and opt for the 5 year term, when maturity date came I discovered that the value per unit is 800 pesos. Naturally I wouldn't want to withdraw my investment just yet. Would they(banks) be able to force me into withdrawing my investment? What would happen in this scenario?

Regards,

Green Horn
December 28, 2012


Dear Green Horn,

In general, UITFs are still the best investment vehicle for the "ordinary" investor since they offer a convenient and relatively inexpensive way to diversify. At least until something better becomes available (like lower-cost index ETFs... hopefully).

• Evaluate UITFs based on fees, performance (% change in NAVPU over time), reputation, etc., but not on the actual NAVPU on any given day. It's misleading to compare NAVPUs of different UITFs because even if they are of the same type, their exact composition may be significantly different. If you're concerned whether a UITF is overpriced or not, then you should evaluate whether the stocks and/or bonds that comprise the UITF are overpriced.
• There is evidence that superior fund performance is as likely the result of expert fund management as plain dumb luck.
• If the bank whose UITF you have invested in goes bankrupt, you're still entitled to your units. You are the legal owner of your investment, and the bank is just the trustee of your funds and the UITF is not part of its assets.
• I'm not sure if I completely understand your last question, but if you're talking about a UITF investment, then no, I don't see how the bank can force you to divest from the fund.

***

Dear Investor Juan,

First and foremost, thank you for making planning for investments and future financial security easy to understand. I would just like to ask for your opinion regarding the best possible course of action for me to take right now. I am a 22 year old student and I have recently invested a bulk amount of Php 200,000 in an Equity UITF (November). I have also invested in an Easy Investment Program for the same Equity UITF.

Given the continuous growth of the stock market and the upcoming release of the first ETF's in the Philippines, I would just like to know if I should cash out my UITF's and/or

1) Invest in different company stocks listed in the PSE
2) Redirect my funds to the ETF's expected to be launched during the first half of this year
3) Keep my UITF investment as is

Which do you think has the largest potential for  long-term growth, especially for a student like me?

Thank you very much!

More power to Investor Juan!

Stephanie
January 12, 2013


Dear Stephanie,

There's no infallible proof that fund managers can consistently outperform the index over a long period of time, and we are 100% sure that a 0.5% trust fee is better than 1%. So if a lower-cost (i.e., has lower fees) fund such as an index ETF becomes available, I suggest transferring your investment to that.

Until then, don't redeem your units until you need the money, or have some better use for it.


***

Dear Investor Juan,

I just started last 2011, I all ready have at least Php 200,000.00 in the bank and currently Php 100,000.00 is in a time deposit. I also have a sun life mutual fund I current still paying. My dad want me to put the other Php 100,000.00 in a time deposit but in the current percentage the bank is offering its not worth it (it too low). The bank offered me to invest it in Peso Money market fund , peso bond fund , GS fund , Peso fixed income fund , Peso balanced Fund , Equity Fund. 1st off , I don't really know all of that. I would like to invest if possible but since i can't understand it. I kind off hesitant to invest.

Can you give me an idea on how should i invest? I know that the Philippines economy is getting better and will get better in the near future. I think it is good to invest in stocks. What direction should i go?

Also will the peso dollar exchange rate decrease? I would like to buy dollar if possible and also invest it.

If you have article i can read for reference it would help me a lot. I would like to risk my money but since i don't have an idea I can't. Also that some of the mention fund and bond that the bank is offering the minimum is 100,000.00 and 10,000.00.

Regards

Carina
January 21, 2013


Dear Carina,

It's impossible to accurately predict how the economy will perform in the near future. So-called experts can't do it, and mere mortals like us can't as well. Same goes for exchange rates.

The very LONG term is a different story, however. In 30 years or more, it would be safe to bet that advances in technology and increases in productivity will result in significant economic gains and greater wealth. In 30 years, life should be significantly better than it is today. Well, if it doesn't turn out that way, then we'll have more serious concerns than investment returns.

Given this premise, your investment decision should be determined by your risk preference and your investment horizon.

If you want zero chance that you'll lose principal, then invest in time deposits, t-bills, or money market funds. Also, these investments would be best if you'll need the money soon, like in five years or less.

If you can afford a bit of risk or are investing for the short or medium term, then invest in a fixed income fund or individual bonds.

Finally, if you have a long investment horizon, like at least 10 years, although longer would be better, then invest in an equity fund.

The Men Who Made Us Fat

Health is wealth. No truthier words have been spoken.

The 30-60-90 Approach to Retirement Planning, Part 3: Adjusting the Savings Formula for Different Saving Periods

In Part 2, we have seen that using the 30-60-90 approach, and assuming an annual real investment return of 4.7%, you should save an amount equal to

Savings = Expenses/4

Where "Expenses" is your estimated monthly or yearly retirement expenses at today's prices.

But what if you don't closely fit the 30-60-90 scenario? What if, for whatever reason, you decide to start saving for retirement much later, like say, age 40? How can we adjust the savings formula above to better reflect your decisions?

Starting to save for retirement later than age 30 will obviously result a higher savings amount since you'll have less earning years to prepare for the same amount of retirement expenses. If you start at age 40, for example, then your savings for the entire year should be enough not just for year 60--your first year of retirement--but also a portion of your expenses in the following year. Furthermore, whereas in the 30-60-90 scenario all your retirement fund deposits have a 30-year horizon, starting later shortens your investment horizon correspondingly and exposes your retirement portfolio to greater risk.

To adjust the savings formula in order to reflect a variable saving period y, take the following. Assuming constant prices, you expect to spend an amount E every year starting on your 60th birthday--the beginning of retirement--for 30 years until you turn 89. You plan to finance your retirement by contributing an amount S every year to your retirement fund, starting on your (60 - y)th birthday, for y years until age 59. If your retirement fund earns a real rate of return r, then the future value of all S payments should equal the present value of all E expenses on your 59th birthday. In equation form, using the formula for future value and present value of an annuity, we get

S*[(1 + r)^y - 1]/r = E*[1 - 1/(1 + r)^30]/r

Simplifying,

S = E*[1 - 1/(1 + r)^30]/[(1 + r)^y - 1]

(I apologize, this equation can't be simplified any further.)

As an example, if E = 32,000, r = 4.7%, and y = 20, then

S = 32,000*[1 - 1/1.047^30]/[1.047^20 - 1]

S = 32,000*0.4967 = 15,894

Or almost double the savings amount if you start at 30 years old, or just half of the expense estimate. If you use y = 30 as in the 30-60-90 scenario, you'll actually get the original equation S = E/4.

Finally, you can also use the above formula for different saving and retirement periods. If z = the number of years of retirement, just replace "30" by z so that

S = E*[1 - 1/(1 + r)^z]/[(1 + r)^y - 1]

So if you're now 30 years old and you plan to retire by 50 and you retain the planning horizon of up to 90 years old, then y = 20 and z = 40. Using the same E and r,

S = 32,000*[1 - 1/1.047^40]/[1.047^20 - 1]

S = 32,000*0.5584 = 17,868

Remember that these estimates are only for the amount that you need to save in your first year (age 60 - y). For subsequent years, you need to adjust for inflation, like in the Part 2, but this time with a slightly different factor

Savings in Year t = (Savings in Year t)*(1 + g)^(z/y)

So that if you start saving at age 40 (y = 20), retire at 60 (z = 30), and the annual inflation rate is g = 4.5%, then

Savings at age 40: 15,894 per month

Savings at age 41: 15,894*(1.045^1.5) = 16,979 per month

...

Savings at age 55: 15,894*1.045^(1.5*15) = 42,791 per month

As always, figuring out the savings amount is just the first step. To meet your target real rate of return, you should invest your retirement savings in a low-cost equity fund and only redeem your units/shares at retirement and as needed.

Short Answers to Unanswered Questions: "Stocks" vs. "Equity" Funds and Comparing Investment Strategies

DEAR INVESTOR JUAN

Dear Investor Juan,

I was also second guessing myself about retirement savings. Most of my retirement funds are in stocks. I was already thinking about transferring it to BDO Equity UITF and wasn't really sure if that's the way to go. Is it?

How exactly do I do this? Since the value of stocks that I have is about 850. Do I take out 50 per month and transfer that to the UITF? and how about the monthly savings that I have? (around 35/month) 

Sorry po kung maraming tanong. >_< I am just confuzzled now. I really thought that going into the stock market was the best way to earn make my money grow.

Ning


Dear Ning.

When you say that your retirement funds are mostly in stocks, how many stocks exactly? If your funds are spread across ten or more stocks, then your portfolio may already be sufficiently diversified (within the equity asset class) and you can choose to keep your funds in those stocks. To improve your portfolio's level of diversification, just invest future savings in an equity UITF.

If your funds are invested only in a handful of stocks, then you have significant exposure to unsystematic risk. To lower your risk exposure, sell some of your holdings and either invest in many other different stocks or in an equity UITF. How you do it--"one time, big time" or in installments--is arbitrary since there's no indisputable proof that "dollar cost averaging" is a superior strategy, contrary to popular opinion.

Finally, there's no reason to be "confuzzled." You're right, "going into the stock market" is arguably the best way to make your money grow. "Stocks" are the same as "equities"--investing in an equity fund is basically the same as holding a basket of individual stocks. The only difference is that if you invest in a few stocks you needlessly expose yourself to risk that can easily be eliminated with diversification. Again, I emphasize that for retirement savings, investing in a low-cost equity fund in the long term (20 to 30 years) is the way to go.


***

Dear Investor Juan,

Thank you very much for a very informative blog. 

I started investing only last year with a reputable global insurance company, so what i have is an insurance link investment. lately, i have been hearing a lot about mf and uitf, and my curiosity is awakened. thanks for blogs like yours and tv shows which explain everything, i now understand the pros and cons of these better.

I have been trying to do a mock computation of yields through bdo online, and i noticed that if i put my money, say 500k, from Jan. 2 - May 31, 2013 (method a), my gain would be more or less 68k. but, if i invest from Jan. for 30 days (method b), take it out, then reinvest it again for another 30 days, and so on until May 31, my gain would be about 82k. 

what is your take on that?

thank you so much. may God bless you in your advocacy. more power!

Anonymous


Dear Anonymous,

I'm not sure where the problem is, but you should earn the same returns with the two strategies since in Method B, whenever you reenter the fund you would be buying at the same NAVPU as when you last exited. Actually, if you're talking about an equity fund, then you should earn less with Method B because of early redemption charges.

The 30-60-90 Approach to Retirement Planning, Part 2: Considering Inflation and Investment Returns

According to the "30-60-90" approach to retirement planning, since the time it takes to accumulate funds for retirement and the retirement period are both 30 years, the amount that you save in any given month or year will finance your retirement expenses in 30 years. In this post, we'll discuss a simple way to estimate how much you need to save today to be able to finance what you intend to spend in 30 years considering the effects of inflation and investment returns.

Let's say that you estimate that on any given month, you'll need 32,000 pesos at today's prices to support your chosen lifestyle. If we consider inflation, then you have to save more than 32,000 this month so that in 30 years, you'll be able to buy what 32,000 can buy today (maybe you should read this phrase one more time, it can be confusing)--but how much more? The inflation rate is the percent increase in the prices of basic goods and services every year. Specifically, if the price a good or service at time t is Price(t) and the average annual inflation rate is g, then the price of the good after n years is

Price(t + n) = Price(t)*(1 + g)^n

(I hope you're not turned off by the math. Honestly, using a bit of math is unavoidable in practical financial management. I always try to make technical discussions as simple as possible, so I hope you'll bear with me.)

For example, let's say that today, or t = 0, 32,000 pesos, or Price(0), can buy a certain amount of goods and services. In 30 years, or  n = 30, how much money do you need to be able to buy the same amount of goods and services if the average annual inflation rate, g, is 4.5%? Using the above equation,

Price(30) = 32,000*(1.045)^30 = 119,850

Which means that 32,000 today will be able to buy as much stuff as 119,850 in 30 years. Does this mean you have to save 119,850 today in order to to finance your target lifestyle? Well, yes, if you plan on keeping your savings in a piggy bank or under the mattress--if your retirement savings will earn zero or very little interest. But if you keep your retirement savings in an interest-earning vehicle, you won't have to save as much. In fact, if you invest in vehicles that provide returns that beat inflation, then you can even save an amount that is less than your target expense. But how much less?

To take investment returns and the time value of money into account, we need to use the present value concept. If you need an amount Price(t + n) in n years and invest your savings at time t in an instrument that earns a rate of return i per year, then the amount that you have to save and invest at time t is

Savings(t) = [Price(t + n)]/[(1 + i)^n]

Using the same example above, in order to accumulate 119,850 in 30 years by investing in an instrument that earns an average annual return of 7%, then you have to save

Savings(0) = 119,850/[(1.07)^30] = 15,744

Less than half of our original retirement expense estimate of 32,000.

Taking inflation and investment returns simultaneously by combining the two equations above, we get

Savings(t) = [Expenses(t)*(1 + g)^n]/[(1 + i)^n] = [Expense(t)]*[(1 + g)^n]/[(1 + i)^n] 

Where "Expenses(t)" is the estimated monthly or annual expense at time t. With the 30-60-90 approach, t = 0 and n = 30, so

Savings = Expenses*[(1 + g)/(1 + i)]^30

This equation shows that if your annual investment return is the same as the inflation rate, or i = g, then Savings = Expenses, or you have to save an amount equal to your projected future expense at today's prices (32,000 in the example above). If you invest such that i > g, like in the above example, then your savings requirement will be less than your estimated expenses (e.g., 15,744 vs. 32,000). Finally and most importantly, if your annual investment return is less than the inflation rate, such as if you invest in savings deposits, time deposits, or not at all, then you would need to save more than your estimated periodic expenses.

(1 + i)/(1 + g) is a special quantity in finance and economics that is referred to as the real rate of return on investments, for which we'll henceforth use the symbol r. It is the rate of return of an investment at constant prices, or at g = 0. Approximately, r = i - g, so that

Savings = Expenses/(1 + r)^30 

To check, at i = 7% and g = 4.5%, r = 2.5%. If your target monthly expense is 32,000, then Savings = 32,000/(1.025)^30 = 15,256. Not exactly the same as the earlier result of 15,744, but close enough for all intents and purposes.

This last equation shows that as long as you invest your retirement savings in an instrument with a consistently positive real rate of return, then you can save an amount that is less than your estimated retirement expenses. But which instrument can reliably provide a positive real rate of return? Low-cost equity funds, particularly in long-term horizons such as 30 years. I'll discuss this in more detail in a future post, but if you want to look into it now, I suggest reading Jeremy Siegel's Stocks for the Long Run.

In the Philippines, the average annual inflation rate in the past decade is 4.5% and the average one-year change in the PSEi from 1994 to 2013 is around 8.5%. Assuming a PSEi dividend yield of 2%, the average annual return of the market is 10.5%, resulting in an average real rate of return r of 6% per year. For a conservatism, however, we can use a lower estimate for r, such as 5%.

Savings = Expenses/(1.05)^30

Savings = Expenses/4.3

For further simplification, you may want to round the divisor to 4, which is equivalent to r = 4.7%.

Savings = Expenses/4

To summarize, using the 30-60-90 approach and assuming that the average real rate of return of an equity fund is 4.7%, you need to save an amount equal to your estimated expenses divided by 4. It does not end here, though, because in order to realize your estimated real returns, you have to religiously invest your retirement savings in a low cost equity fund and withdraw no earlier than 30 years after.

Finally, I must clarify that the savings amount given by "Savings = Expenses/4" is only for the first month or period of the earning period, or at age 30 in the 30-60-90 framework. In the succeeding years, the savings amount must be adjusted by the annual inflation rate.

For example, if Expenses = 32,000 per month, then

Savings at age 30: 32,000/4 = 8,000 per month
Savings at age 31: 8,000*1.045 = 8,360 per month

...

Savings at age 55: 8,000*1.045^25 = 24,043 per month

But what if your situation does not adequately fit the 30-60-90 scenario, like if you're just starting to save for retirement at age 40? In a follow-up post, I'll show how you can adjust the savings formula to better reflect your situation.

***

EDIT: 2 July, 2013

I checked my numbers again, and the average one-year change in the PSEi from 1994 to 2013 that I got was 8.6%, not 12%. I will make the necessary changes in the above discussion to reflect this difference.