The Interest has decreased but the Capital Repayment has increased, why??

lukekelly_2

Robert_Sterling wrote: »

Have you come across "The Monty Hall Problem"
http://www.youtube.com/watch?v=mhlc7peGlGg
This link is to a Mathematical Problem not to a business.

Sorry, missed this when you posted it initially. It is a puzzle I know well, I sometimes use it when teaching probability to school children (or indeed undergraduates). It's a good example of our awful intuition when it comes to probability! My other favourite example of that is the following question:

How many people do you need in a room to have at least a 50% probability that at least two people share a birthday?

I'll post the answer in a little while.

dave461_2

If your mortgage was the same capital each month it would of started off with higher payments at the start and lower payments at the end to account for the interest on the full amount at the start, and virtually nothing at the end.
So say £200000 mortgage / 22 years / 12 months = £758 equal payments.
But at the start you'd pay interest on £200000, say 3%, £500, so payment would of been £500 + £758 = £1258.
At the end you would only pay interest on the last £500, at 3%, £1.25, so last payment would be £500 + £1.25 = £501.25.
The mortgage just calculates the capital payment so that you pay the same every month including interest.
If your mortgage was 0% you'd pay £758 to pay the money back.
At 3% you only pay £535 capital in the first month and £1030 capital in the last month, but a constant payment of £1035 over 22 years.

lukekelly_2

rjar20rjar wrote: »

To achieve this in a way that they do not need to continually reduce my payments the amount of capital portion of my payment should increase in a linear manner, for example I may pay £5 a month more as capital portion and £5 a month less in interest payment.. At the end of the mortgage term the capital portion will be the majority of the amount being paid each month.

It doesn't work in a linear manner, which is why your reasoning is incorrect. This would work only if interest was a set amount, say £5 a month. It is not though, it's a proportion of the amount of debt left. Hence we have non-linear behaviour.

Interestingly lenders do not seem to reveal the capital repayment model they are using and if they can randomly vary that amount there are no stated parameters (e.g. minimum or maximum) that allow the borrower to anticipate or agree to ... in theory what is preventing them from deciding to double the capital repayment in lean times and half it in good times ?

They do reveal their models, and indeed all use the same relatively simple model. Any spreadsheet software and various websites can calculate it all because the formulae are well-known. They're not quite simple enough to make their workings entirely obvious to everyone, but they're not random or mathematically complex. It's not some hidden secret, and it's easy to predict what changes in interest rate will mean for mortgage payments.

pwllbwdr

You're right on two counts - what you say about lenders and payments is true, but that isn't what this thread is about. The point is that IF the lender immediately adjusted the payment and reduced the interest part of it because of a reduction in interest rate, the amount of capital repayment each month has to go up a little.

pwllbwdr

Sorry - got out of sync - that was to CLAPTON.

benjimoron_2

Not an easy one to explain this, let me try.

As has been said the capital payments have to increase in order to cover the mortgage, this is because with lower interest rates you don't make as much saving on interest near the end of the mortgage so the repayment has to go up to a higher level at the start (but will be lower at the end, compared to higher interest rates).

Imagine this:

You've got a £100,000 mortgage @ 5% and the repayment part is approx £100 a month. Now let's assume that the interest rate of the mortgage dropped to 0%. If the repayment stayed at £100 a month you'd be paying £1200 a year or £30,000 over the 25 year period. This would leave you £70,000 short of paying off the mortgage. So the repayment part has to increase in order to keep the amount you pay each month (total, not just repayment part) consistent across the whole mortgage.

Most people don't understand this, I don't mean any offence by that it's just a fact that even when explained alot of people can't understand it. It'll either click at some point or you'll have to accept that the repayment part has to increase when the interest rate goes down.

It works the other way too, if the interest rate went up to 100% then you'd be paying virtually no capital at the beginning of the mortgage, but near the end you'd be paying far less interest therefore in the final few months your repayment amount would be huge. You'd pay off most of the mortgage in the final year alone. Your interest would be much lower than it had been in the previous years and your repayment part would go up.

rjar20rjar

This is fascinating, it all makes sense and the maths is actually very simple, it is just that no-one has posted the formula to actually show that. Having looked at the amortization calculator and compared that with my payment model it is indeed true that when the interest rate is high the lender starts with a low capital repayment and increases that each month by a larger amount than when the interest rate is low and the ;ender starts with a higher capital repayment with a lower increase each month. So at 4% it might increase by £2 a month and at 2% at £1 a month.

If the interest rate was changed to 1% today how is the first new capital repayment calculated (i.e. what is the formula) ? Or is it that the increase per month is calculated and the first capital repayment is calculated from that ? What is the equatoin that relates the interest to the amount owed to the term to the first capital payment ?

Now the question is why ? why not keep the same payment structure regardless of the interest rate (i.e. start low and increase by a greater amount), the mortgage would be paid off in the same time, the monthly payment would better reflect the increase or decrease in the interest rate. The most plausible explanation is that the lender wants to keep the cash coming in and balances the capital to offset the loss in interest.

rjar20rjar

I guess this is something you just have to work through so I will answer my own question. It is a linear equation but the rate of decrease in interest payments/increase in capital payments is related to the interest rate charged., the higher the interest rate the faster the increase in capital payments has to be. The interest payment has to equal 0 by the end of the term. The spreadsheet PMT function can calculate these amounts.

The example being that an interest payment of £500 a month has to decrease to £0 on a term of 230 months slower that an interest payment of £1000 a month over the same term if the monthly mortgage payment has to remain the same. The capital has to correspondingly increase at the same rate to equal the monthly payment at the end of the term.

Would have been nice for the lender to point this out at the time.

pwllbwdr

No. It just doesn't work like that. The "payment structure" is exactly the same, it is just that the repayment of capital HAS to be more front-loaded at lower interest rates. If you insist in persuading yourself it is sharp practice on the lenders' part, I'm afraid you are deluding yourself.
Rather than quoting formulae, I'd suggest that the best way to convince yourself of this is to set up a simple spreadsheet. It is a series of discrete payments (monthly) rather than a continual supply of money, so it really does lend itsef to spreadsheet analysis.

There are formulae which can be used to calculate the required payment for a given term and interest rate, but simply quoting these will not explain nor help you understand why it needs to be so.

pwllbwdr

Sorry - intervening post. I'm not sure what you think is linear. The decrease in interest over time is not linear.