Fixed instalment versus constant amortisation

In the fixed instalment system you pay the same amount every month from first to last; what changes inside it is the split, with interest heavy at the start and amortisation heavy at the end.

In the constant amortisation system it is the amortisation that stays the same, so the instalment starts high and falls every month, because the interest is charged on a balance that keeps shrinking.

Yes, and there is even a closed formula for it: the amount financed times the rate times the number of instalments plus one, divided by two. On three hundred thousand at zero point nine per cent a month over three hundred and sixty months, that is four hundred and eighty seven thousand three hundred and fifty against seven hundred and twelve thousand two hundred and twenty one.

What does not follow is that it costs less. Adding up interest with no discounting compares money from today with money from thirty years out as if they were the same, and that is where the argument breaks.

At the rate of the contract itself, neither. Discounted at that rate the two plans are worth exactly the amount financed, to the cent, because that is what an amortisation schedule is: the set of payments that clears the debt at that rate.

What decides is the rate your own money would earn. Below the contract rate the constant amortisation costs less today; above it the fixed instalment does; exactly at it they tie. That is the comparison this page runs with the rate you type.

Because it pays back more principal from the first month. The amortisation is the amount financed divided by the number of instalments, every single month, while in the fixed instalment system the early amortisation is tiny and most of the payment is interest.

On the example above, the instalment starts at three thousand five hundred thirty three against two thousand eight hundred eleven, and only drops below it on instalment ninety eight. Those first eight years are the real cost of paying less interest later.