The bank offers 1 year at 5.29% and 2 years at 5.49%, and everybody compares the two numbers and takes the smaller one. But those are not two prices for one thing. Taking the one-year leaves you standing at the same desk in twelve months, and what you pay then is a number nobody has yet.
So it is a bet, and a bet has odds you can work out. There is exactly one rate for the second year at which the two cost the same, and it falls straight out of the compounding:
(1 + r1)(1 + f) = (1 + r2)2 → f = (1 + r2)2 / (1 + r1) − 1
At 5.29 and 5.49 that is 5.69%. So the one-year is the better choice only if the one-year rate a year from now is under 5.69 — which is 0.4 of a point above where it stands today. A rising card is not a discount for committing. It is the price of a rise the market has already put in, and fixing short is a bet that the rise is smaller than that.
The number below will be a couple of hundredths off that one, and both are right. The identity above is pure compounding; the page also solves the same question on your actual amortising balance, where you are paying the loan down while all this is happening. They agree to about two hundredths of a point, which is a useful thing for two independent derivations to do.
Nothing here is advice, and nothing here forecasts a rate. It works out what your choice is betting on and what being wrong costs, and then it stops. Nothing is stored: this page has no database and no session.
Your loan
Taking the 1 year instead of the 2 years is a bet that the rate then will rise by less than 0.42 of a point. It is 5.29% today. Nothing on this page forecasts that number — it works out what your choice is betting on and stops there.
What each term is betting on
| Term | Rate | Needs it under | A move of |
|---|---|---|---|
| 1 year | 5.29% | the baseline | |
| 2 years | 5.49% | 5.71% | +0.42 |
| 3 years | 5.65% | 5.85% | +0.56 |
Above the level line the longer fix is ahead by that much; below it the 1 year is. Each line crosses once, at its own breakeven. Today's rate is marked, so which side of a crossing you are standing on is the answer.
What is left owing after the 2 years
| If the rate goes to | 1 year | 2 years | Difference |
|---|---|---|---|
| 3.29% | $469,840 | $481,765 | $11,925 1 year |
| 4.29% | $474,745 | $481,765 | $7,020 1 year |
| 4.79% | $477,215 | $481,765 | $4,550 1 year |
| 5.29% today | $479,696 | $481,765 | $2,069 1 year |
| 5.79% | $482,189 | $481,765 | $423 2 years |
| 6.29% | $484,693 | $481,765 | $2,927 2 years |
| 7.29% | $489,736 | $481,765 | $7,970 2 years |
The 1 year at 5.29% and the 2 years at 5.49% only make sense together if the market expects the rate after the first stretch to be about 5.69%. That is what a rising card means: it is not a discount for committing, it is the price of the move the market has already put in, and fixing short is a bet that the move is smaller than that. On your actual loan the crossing lands at 5.71% rather than 5.69% — pure compounding ignores the fact that you are paying the thing down while it happens, and everything above uses the loan's own number.
On $500,000 over 24 months, with the same repayment either way, taking the 1 year leaves $7,970 more owing at the end of the 2 years if the rate goes to 7.29%, and $11,925 less if it goes to 3.29%. The two ends are different sizes because the breakeven is not in the middle of that range — it sits at 5.71%, so there is more room to be wrong on the downside side.
Half on each term costs the average of the two paths — it cannot beat both, and it cannot lose to both. What it does change is the size of the jump: when only half comes off a fix at once, a two-point rise moves the repayment by half as much, and it moves twice, a year apart. That is a real thing to want, and it is a different thing from paying less.
If rates rise, a long fix was right and you keep it. If they fall, you can break it — and the bank charges you its loss on the wholesale rate, which is roughly the fall multiplied by what is left of the term. So the good case is capped and the bad case is paid for. This page does not compute break costs: the formula is the bank's, it uses wholesale rates on the day, and a number invented here would be worse than none.
That is what clears $500,000 over 300 months at 5.29%, the cheapest rate on the list. That is why the answer here is a balance rather than a pair of totals: the same money leaves the same account either way, and the only thing that differs at the end of the 2 years is how much loan is left. If you let the bank reset the repayment at each refix instead, the difference shows up as a smaller payment rather than a smaller balance, and it is the same money.
What it does not know
It does not forecast rates. On purpose, and it is the whole discipline of the page. It computes the number your choice is betting on. Whether that bet is a good one depends on things no arithmetic here can see, and anybody who tells you otherwise is selling something.
Interest compounds monthly here. A New Zealand bank accrues daily on the balance and charges monthly, which lands a few dollars apart on half a million over a year. The comparison between two terms moves by less than that, because both sides shift the same way.
Cash contributions are not in it. A bank paying you two or three thousand to come across is worth more than the whole rate difference over two years — but it is paid for moving banks, not for picking a term, so it lands on both paths and cancels out of this comparison. It does not cancel out of the decision to switch, and it usually comes with a clawback if you leave inside three or four years.
Break costs are the bank's formula, not this one. Roughly, the fall in the wholesale rate multiplied by what is left of the term — but the inputs are the bank's, on the day. A number invented here would be worse than no number, so there is not one.
The card moves. Rate sheets change between Tuesdays, and the one you are offered is often not the one advertised. Every figure here belongs to the numbers you typed in.
It has no view on what you should do. Certainty is worth something, and how much it is worth to you is not a number this page has. A fix you can afford at the top of the range beats a cheaper one you cannot.