What is a million dollars worth? If I were to offer a million dollars today of course the value would be a million, but what if I gave $500,000 today and $500,000 in ten years time? Still the same? What if I gave you a note promising that I, and my descendants would give you, and your descendants one dollar a year for a million years? Obviously inflation, the amount you could get if you invested the money today, and a myriad of other factors mean that the value of money has a time-factor, it is better to have money now rather than later.

Any financial text book will give the formulae that apply here, but it is the ignorance of the time value of money that leads many people to make poor investment decisions, especially when the question of paying off the mortgage or investing in something else comes up.

A very common piece of advice given on how to save money on your mortgage is to make more payments, pay more now and save all that interest later. The bank simulator shows that by "tailoring" your home loan, which usually means giving the bank more money and sooner, you are able to save many tens of thousands of dollars.

Yes, it is tempting to want to give the bank that money, because $20,000 is certainly a lot of money... today. What will it be worth in 20 years?

A simple calculation can be made, straight out of a text book. Just say the annual interest rate is 8%, compounding interval is monthly, over 20 years. The formula for the present value (PV) is
PV = FV * (1 + i/m)^-mt
where PV = present value = ?
FV = future value = $20,000
i = nominal interest rate = 8%
m = number of compound periods in a nominal period = 12
t = number of nominal periods = 20
PV = 20,000 * (1 + 0.08/12)^-(12*20)
which equals $4059.43.

If you gave me $4,100 today, you should expect at least $20,000 back in 20 years as an absolute minimum, but most people who don't run the numbers would be overjoyed at such a return on their investment. Do this calculation with the tens of thousands of dollars you will save on your mortgage with your "tailored home loan" and then you will see just how unimpressive this really is. A $20,000 debt due in 20 years at that interest rate really is worth only $4,059.43, and if you wanted to sell an IOU to a bond investor with these terms, $4,059.43 is all he would give you for it. If inflation rose to double digits, as it has done many times this century, the capital value of such an annuity would fall dramatically. The real return, that is the after inflation return would be negative. If you invest in bonds with an interest rate lower than inflation you lose money.

This figure isn't just some theoretical number crunch unworthy of any attention in the real world, just think of what a house was worth in the 1950s, in today's money this isn't really very much. That is inflation for you, the amount of money you dream of one day earning will be starvation wages in 50 years.

And here is another calculation. An annuity is a cash flow producing instrument, like a bond.
How much is $500 paid annually over 10 years worth, if the interest rate is 8% per annum, compounded monthly? On face value this is worth $5000, but the future value of this annuity is
FV = F[(((1+r)^n)-1))/r]
where FV = future value = ?
F = annuity per compound period = $500
i = nominal interest rate = 8%
r = i/m = 0.08/12
n = number of nominal periods = 10
Future value = $5152.69. This annuity will produce $5000 cashflow, but this is equivalent to a single payment of $5152.69 in ten years.

This gets more interesting when you look at the present value (PV)
PV = F[1-((1+r)^-n))/r]
so we plug those values in and find that this annuity is worth only $4821.45 today.

So now we look at something directly applicable to mortgages and the idea of paying them off sooner. An equivalent income stream calculation shows the equivalent cashflow of an annuity running for different periods of time.

A home loan runs over a period of 30 years. Repayments are $800 a month. What is the equivalent income stream such that the mortgage is paid off over 20 years instead? To calculate this we work out the PV of the 30 year mortgage and solve for the payments of the 20 year mortgage. Payments are monthly, interest 8%, compounded monthly.

PV = F[1-((1+r)^-n))/r]
F = $800
r = 0.08/12
n = 360 (=30 years x 12 months)
PV = $109,026.80
Now using this PV we solve for the new F, where n = 20
Payments are now $911.94 a month, over 240 months.

You pay $218,697.60 over the course of 20 years, as opposed to $288,000 over 30 years.

I will stress that these two series of cash flows are financially equivalent. They have the same present value, and the interest rate is the same. The argument that you are saving $70,000 in this case is false, and preys on people's ignorance of the time value of money.

What does all of this mean to mortgagees?

Sometimes people email me asking whether the above is actually a recommendation that you don't pay your mortgage off.  Actually my point was mainly that the big numbers the banks claim are somewhat exaggerated from a time value of money perspective.  If the bank says you'll save $200,000 in interest payments they are telling the truth: in nominal dollars that is presumably what their calculations show you will save.  However from a time value perspective $200,000 in 20 years time is actually not quite so much money as it may seem.  $200,000 may buy you a new Porsche today, but that's probably going to be only enough to buy an average family car in 20 years.

I especially want to make the point that the big numbers the banks point out in their marketing aren't that impressive when you consider that if you invested the same cash elsewhere (like in a share portfolio for instance) the numbers would be at least as big.  (Of course paying your mortgage off is a good idea if the only other alternative would be squandering it in some way.  A lot of the "mortgage or invest" discussions hinge on the assumption that you will actually invest, they aren't generally proposing from a financial point of view at least that the extra payments should be used to buy yourself a luxury car. 

Banks want people to pay off mortgages early so they can write more loans, the money is usually in application fees and the like since interest rate spreads aren't huge in today's competitive lending environment.  They also want to reduce their credit exposure and have some way to identify loans which are in default.  The bank's motivation however is of only passing interest to you though.  Transactions can be win/win, win/lose or lose/lose, so you shouldn't necessarily assume that everything he bank does for it's own benefit is necessarily to your disadvantage.

I generally frame my advice to clients in the following terms:

If you have $10,000 cash to invest and are thinking about whether to put it into the mortgage or investment, you actually may be forgetting that there are other choices.

If you put the money into the mortgage and then redraw it to purchase some investments, you would be in essentially the same position as you'd have been if you had invested directly (you have a $10,000 debt and $10,000 worth of investments, except now that $10,000 debt would have tax deductible interest.  

(Of course a loan facility that allows redraws may be required, or perhaps you'd want to set up a margin loan.)

Another option might be to spend that $10,000 on your living expenses while telling the boss to increase your superannuation contributions via salary sacrifice.  Because you would only be paying 15% tax on the super contributions ("contributions tax"), instead of your marginal tax rate would could be anything from 0% to 46.5% but for most people is at least 31.5% or 41.5%.  (These are 2007/08 tax year rates I'm quoting by the way... )

Because you are saving all that tax, the amount you could afford to contribute to super would be much greater.  You would contribute the pre-tax sum which after tax would give you the $10,000 you would otherwise be dependent on for living.  For instance if your top marginal tax rate was 41.5%, you would be able to package over $17,000 into super. (41.5% tax on $17,000 = $7,000).  15% tax would be taken off that by the super fund leaving $14,450 to go into super.  The earnings on this will be taxed at only 15% until you retire, and then when you turn 60 you could withdraw that money tax free (if you want to) and pay off the mortgage then.

In the calculations I do for my clients, taking into account the after tax cost of debt, conservative return assumptions, risk profiles etc etc, I usually find that the best thing to do is superannuation salary packaging/deductible super contributions, then paying off non deductible (i.e. personal) debts, then making an undeducted contribution to super, then buying growth oriented, managed funds, shares or property, then paying off deductible (investment) debts and finally just accumulating cash.

Those are typical findings, but of course some people have complicated situations.  There may be penalties for paying debt off early, you may have already fully taken advantage of the superannuation contributions limits and not be entitled to invest any more, your risk tolerance may be extremely low and so you wouldn't dare invest in anything more aggressive than cash, etc.  Since everyone is different, at this point I'd have to add the disclaimer that if in doubt you should seek personal advice, because everything in this FAQ is of a general nature only.

Needless to say if you are earning less interest on your cash deposits than you are paying on your debts, its usually not a good idea to horde large amounts of cash when you at least have the option of paying off the mortgage.  If you don't have a line of credit or mortgage offset account you may want to keep some cash at hand, but I generally don't recommend people hold tens of thousands of dollars in cash accounts when they could save more interest than they could earn by paying off the mortgage.