We're looking to buy our first house, and are considering the different options for a mortgage. We are in the UK. We're having trouble comparing the options because it seems that you can only tell what your repayments will be for the first 2, 3 or 5 years. Is there any way of calculating (even a rough guess) what they will be after the fixed period?
You can get a guess by looking at interest rate futures. It looks like UK adjustable-rate mortgages are based on 3-month LIBOR, according to http://www.mortgages.co.uk/Libor_Mortgages/Libor_Mortgages.html. If this is the case, you can look at the Eurodollar futures rates to get see what the rate is predicted to be. The interest rate will adjust to some amount above this, which depends on the specific mortgage.
Looking at http://tfc-charts.w2d.com/marketquotes/ED.html:, the last trade for December of 2012 (when I write this) is 98.9750. To get the predicted LIBOR, subtract this from 100. 100 - 98.9750 = 1.025%, so rates are still predicted to be low.
For December of 15, the last trade is 96.5950. So the predicted LIBOR would be 100 - 96.5950 = 3.405%.
This is a the market forecast, no one know what the rates will be at that time, they could be higher or lower.
If the margin on the loan is 3%, then the rate in the first case would be 4.025%, and in the second case 6.405%
What the monthly payment will be depends on a few other factors as well, the main one being how long the loan is (technically, the amortization time.)
http://www.interest.com/content/calculators/aprCalcARM.asp is a good calculator to do the computation. Note that the "expected adjustment" gets applied every year, so if you start it at 5% for the fixed period, and make the adjustment 1%, it will go up 1% every year until it hits the cap. You can make the cap 6% if you want to only have it adjust once. If you want to put in multiple interest rate changes, http://www.vertex42.com/ExcelTemplates/arm-calculator.html will let you put in more detailed info.
No prediction can be perfect. But the bank gives you a hint what they expect: The bank offers different terms, but the bank expects to make the same money, no matter what you choose.
So if five year fixed rate is higher than two year fixed rate, then the bank expects that those on two years fixed will have to pay more when they renew their mortgage, so the bank would expect the rate in five years to be higher than today. If five years fixed rate is the same as two years, then they expect the rate to stay the same or drop. Of course that's what the bank expects, not necessarily what will happen.
As already pointed out, using futures contracts data is your best option for the first 5/6 years - this is how far futures contracts go into the future. For the period of time not covered by futures, using historical data can be useful.
I just published a free adjustable rate mortgage calculator to do exactly that.