CPF and the annoying thing about compounding

COMPOUNDING interest will make you rich, they tell you. A cornerstone argument of personal finance and wealth managers, compounding interest - that is, money snowballing into Warren Buffett-like billions - is a seemingly unassailable argument for the need to save, and start early, and to invest with so and so or put your money in that financial product.

Just let compounding work its magic, goes the argument.

A popular rule of thumb to determine how long it takes for your money to double is known as the rule of 72. Essentially, take an interest rate, say 7 per cent a year. Divide 72 by that number - you get around 10. That means at a 7 per cent interest rate, your money will double every 10 years.

Sounds good? As 19th century Irish writer Oscar Wilde would say, the truth is rarely pure and never simple.

The most annoying thing about compounding is that its effects are only felt at the end.

In the words of the motto of a well-known boys' school here, "the best is yet to be".

Theoretically, money makes more money. You gain interest on a sum of money one year, and gain interest on that interest the next in addition to interest on the original sum.

The truth of the matter is, compounding starts off painstakingly slow, and only becomes truly spectacular right at the end.

And we all know what happens in the end, thanks to British economist John Maynard Keynes: "In the long run, we are all dead."

People can thus be forgiven for getting a little bit impatient with the compounding genie. All it makes are promises after promises without seeming to deliver much.

This is best illustrated with a current example.

Singapore's own Central Provident Fund (CPF) has been in the hot spot lately for purportedly giving low returns, insufficient for Singaporeans to meet their retirement needs.

Adding to the angst is the fear that more and more money will be locked away.

Currently, just about half of Singaporeans meet the minimum sum to qualify them for the maximum lifelong annuity payout called CPF Life. The minimum sum is now at $155,000.

But the government has said that most young Singaporean wage earners today will be able to meet the minimum sum by the time they retire, provided they buy property within their means.

An independent study on retirement commissioned by the Ministry of Manpower and conducted by National University of Singapore professors have also found that young workers today can replace their income upon retirement at rates similar to developed countries.

So why is there a disconnect? Why do the young feel that they will never be able to hit the minimum sum, even while studies have shown they can?

Part of the answer, perhaps, lies in how compounding works.

There are two main accounts everybody has in the CPF to deal with retirement: the Ordinary Account (OA) and the Special Account (SA).

At age 55, money from the OA and SA is transferred to a newly created Retirement Account. Any monies in the RA in excess of the minimum sum can be withdrawn. Otherwise, the remainder is used to buy the CPF Life annuity.

However, come age 55, people might not have enough in the OA to speak of.

Money there is typically withdrawn to buy a house, and then to upgrade to a bigger house, and so on.

That might leave the heavy-lifting for the minimum sum to the SA. The sum of money there, if you haven't lost it trading stocks, theoretically accumulates at a steady pace of at least 4 per cent a year.

The accumulation gets faster towards age 55 because the proportion of your wage that goes into the SA every month increases with age.

It starts at 6 per cent when you are below 35, and rises steadily, peaking at 9.5 per cent from age 50 to 55.

For a typical young person today, how much would he have in his account by age 55?

Basic assumptions

Let us assume our young chap starts off work earning the equivalent pay of a university graduate.

This is not an unreasonable assumption. About half of Singapore's 2.1 million strong resident labour force is currently either a diploma or equivalent holder (18.4 per cent) or degree holder (31.5 per cent), as of 2013.

The proportion of diploma and degree holders get larger if you zoom in to look at the data of younger age groups.

Out of the 210,000 economically active residents aged 25 to 29 last June, over half, 106,000, are degree holders alone. Another quarter, or 53,000, have a diploma or professional qualification.

According to the most recent graduate employment survey, the typical starting salary of a graduate is $3,000 a month.

The median wage of a typical resident, too, was at $3,250 a month last year.

To be conservative, let's start with a $3,000-a-month wage assumption, which adds up to $36,000 a year.

To be even more conservative, we don't factor in bonuses. No 13th month pay, no commissions, nothing.

The next assumption we have to make is how much wages rise by every year. Nominal wages have risen by an average of 4 to 5 per cent a year for the past five years, including the 2009 recession.

Again, let's peg wage rises conservatively at the core inflation rate of 2 per cent.

Our average young worker thus begins working at age 26. By the end of his first year of work, he has $2,160 in his SA. So his SA increases by slightly more than $2,000 every year, plus interest.

Fast forward 10 years, at the end of age 35, and he has just $28,000.

This is still a far cry from the minimum sum, however. And it's been 10 years.

Even at age 45, when another 10 years have passed, his SA stands at around $80,000.

Who knows what the minimum sum will be, then? His SA is increasing at a faster pace, but it still seems slow, and it is still half of the minimum sum of about $160,000 today.

So it took us 20 whole years to get the first $80,000.

But something dramatic happens to the numbers in the last few years of compounding, further boosted by an increase in the SA contribution rate.

This assumes, of course, that our hypothetical male person keeps his job and does not have to take a pay cut.

While it took 20 years to hit the first $80,000, it will take a mere 10 years to accumulate the next $100,000.

When our chap is 55 years old, he will actually have more than $180,000 in his SA.

While he accumulated just $2,000 to $3,000 in his SA every year in the beginning, the final two years will see him add $12,000 a year to his SA - all on conservative wage growth assumptions.

The way the numbers work is not intuitive. Nor can one easily understand the power of compounding from the vantage point of the 25-year-old, the 35-year-old, or even the 45-year-old.

The second most annoying thing

This sum of $180,000 will probably be lower than the minimum sum in 30 years' time.

Assuming it increases by core inflation of 2 per cent every year, our fresh graduate will need close to $300,000 by the time he hits 55.

Then again, the minimum sum might yet be met if we relax our conservative assumptions.

We also left out the role of the OA in providing for retirement savings altogether.

Assuming he buys a modest-sized flat costing about $400,000 with his wife of a similar earning capacity and age, right at the beginning of his working career, it is entirely possible that the couple can pay off their mortgage by age 45.

That leaves an additional 10 years in which the OA will add at least $80,000 to one's savings, without factoring interest. This adds up to total retirement savings of around $260,000 in the CPF.

And who knows, maybe he will get a promotion at work, and a pay rise in the earlier years. This leaves even more years for compounding to do its work.

And so we get to the second most annoying thing about compounding: the assumptions you use matter a lot.

The way the math works is that any seemingly small change every year will add up to exponential growth over dozens of years.

Wage growth of just one more percentage point, for example, will add $30,000 to the SA and another $20,000 to the accumulated OA from age 45 to 55.

In an optimistic scenario where wage growth is also 5 per cent, one will have $285,000 in the SA at age 55, and have an extra $170,000 in the OA accumulated between age 45 and 55.

This is more than one and a half times that of our base case scenario.

If one tweaks starting salary to $4,000 a month and keeps wage growth at 5 per cent a year, you end up with $380,000 in the SA at age 55, and an extra $225,000 accumulated in the OA - more than enough where the minimum sum will probably be concerned.

Young investors and savers can thus draw a few lessons from how compounding works.

First, don't expect to see results early.

When you are rolling your snowball, the first 10, even 20 years will seem frustratingly slow. It is easy to get impatient and deviate from, say, a blue-chip, conservative investment strategy and take bigger punts with penny stocks that give you a higher chance of failing.

Staying the course is more likely to reward.

Second, ensure your assumptions are conservative.

Being conservative has advantages. The chances of you being disappointed fall, and the chances of you being pleasantly surprised rises.

Some investment schemes might promise returns of 10 per cent a year or more. Many pension funds in the US were operating on the assumption of 8 per cent returns a year. This is unrealistic, as many are finding out.

A steady rate of return of around 4 per cent is probably safer.

Finally, work hard to boost returns early on.

Getting as high a starting salary as possible and socking as much away as possible to begin the process of compounding is probably the best strategy for younger folk hoping to retire comfortably before they are 55.

Whatever you do, and whatever your aims, the returns might not seem like much at the start. Once critical mass is reached, however, they might seem more than enough.