For example, if you borrow 200 000 over 30 years at a rate of 5, your monthly repayments would be around 1074. Over 30 years, you would actually pay 1074 x 360 (months), which is 386 640.

That's 186 640 in interest!

If you could find an extra $246 a month, and pay 1320 a month into the mortgage, you'd cut 10 years off the repayment period the loan would be fully paid in only 20 years. Moreover, your total payments would be 316 664, saving 69 756!

The flaw in this technique is that it ignores the time value of money.

Everyone knows that money is worth less now than it was when they were younger. If you take that 1074 mortgage repayment, for instance, in 30 years time, when the last payment is due, it would only be worth 437 in today's money.

A dollar now is always better than a dollar in a year's time, or in 10 year's time.

How does the time value of money affect our example?

You cannot simply subtract the mortgage interest amount for a 20 year mortgage from the interest on a 30 year mortgage. What you need to do is calculate the Present Value of each mortgage.

The Present Value of a 30 year mortgage with repayments of 1074 at a 5 interest rate is 200 066.

The Present Value of a 20 year mortgage with repayments of 1320 at a 5 interest rate is 200 066.

The two repayment schemes are exactly equal.

The 69 756 'saving' in the interest rate is really just the effect of adding the extra 246 a month into the repayments - in fact, that 246 a month adds up to 59 040 over 20 years.

What if you took that 246 a month and invested it in, for example, mutual funds?

If you could get a return of 10 p.a., after 20 years you would have 186 804. With inflation at 3, that would be worth 102 597 in today's money.

Why would the banks recommend that you pay off your mortgage quickly? Surely the longer the income stream lasts, the better?

The banks love being able to prove that their recommendations will 'save you money'. But in reality, the banks do understand the time value of money. They know the true value of that extra 246 a month that you're giving them now, not in the future. And the shorter the time you take to repay the mortgage, the lower their risk, and the sooner their money comes back to them to be loaned out again.

There are some arguments for paying your mortgage back quickly for one thing, the quicker you pay, the quicker your equity grows. But you should understand that every dollar you give the bank now is a dollar that you can't invest.

Giving your money to the bank to avoid paying 5% interest means that you can't use that money to earn 10 or 12 or 15 somewhere else.