I struggle to follow the exact interest calculation of my boyfriend's mortgage. His mortgage is with Nationwide, and when I rang them I got the very exciting information that "the amount of interest he pays depends on the interest rate and the amount he ows". Aha. They were not able (or willing) to give me a more precise answer.
It's easy to derive the monthly payment for capital and interest with the standard formula (same result as bank). But I would like to track all mortgage transactions, including overpayments etc. How exactly is the daily interest calculated? Do banks here in the UK operate on the basis of 360 or 365 days per year? Is the interest added to the account daily, and how exactly is the daily interest rate derived?
All my friends are clueless as well. They even suggested that the daily interest rate might change daily (???).
Beware, there are numerous ways of doing it.It depends when the interest is charged to the account.
By 365 (why 360?). Leap years are also still 365 unless the nominal quoted rate is quoted other than as 'per year'..
No. That would mean an enormous debt.
(Amount owing x annual interest rate /365) is calculated every day and accumulates on a daily basis until the end of charging period which is usually annually but can also be monthly or quarterly. Note the 'interest rate' quoted above is NOT the APR.
If linked to base rate then this is possible, but unlikely these days.
I'm with the Halifax, and had to transfer a chunk of money (£8k) off mine last week - I went into the branch, and the girl doing the transfer had to check with their mortgage specialist about how best to input it to the system so we'd see the benefit of it. Apparently unless they do a transfer in a particular way it gets allocated differently ?!?
It brought into question how the small overpayments (~£75 a month) we make are being allocated - they show up on the statements, but given that these are only small amounts, as long as they show up eventually they wouldn't make a whole hill of beans difference.
It may depend on the exact terms of the mortgage how funds are allocated - for instance we originally took ours out in '91 but we remortgaged, changing it to a repayment about 2 years ago, without changing the repayment period from the original projected term.
As part of the "security" process I was asked when we first took it out - which as far as i'm concerned should be irrelevant - as we'd moved it to a complete new mortgage 2 years prior, but they happened to mention two different "pots" that the money had come out of being charged at different rates for some unknown reason.
In short, I haven't got a clue, and it would appear they don't either unless you touch lucky :-}
Yes. Some lenders will either regard the lump sum as some monthly payments in advance and others as an immediate reduction in the amount owed. Silly, I know, its a relic from the old b/soc days.
In fact, whilst it might not be a large ill, it could be a substantial hillock.
Yes, Ahem, it's very difficult, only highly trained actuaries can understand it, you are too stupid etc, etc. A pretty young thing such as yourself shouldn't be worrying about such things ;o) Sniff,Sniff something smells funny.
I was going to joke that you probably have a finance PHD, but I googled and you do, don't you.
Well I did try to reverse engineer my mortgage calcs with nationwide and the nearest I could get was using their rate as annual with a day count of ACT/360 and even then my calc was slightly low, so maybe they also use some kind of rounding up.
Try writing to Nationwide, you might get an answer. If you do please post as I've been meaning to do it for years but am too lazy.
An old banking trick. I tried to work out the interest once on a commercial finance deal for a major project. As I got different answers from the Bankers involved, I enquired and was told that the daily interest was calculated as 1/360th of the annual rate.
Using a daily interest rate of either 1/365 or 1/360 of the annual rate implies simple interest. Do banks not usually use compound interest, in which case should the daily interest rate should be a more complex formula.
To use a simple example, if £100.00 is borrowed at 10% per annum then after 1 year, if no repayments are made, the total outstanding should be £110.00. But using the 1/365 method and calculating interest daily then after one year the total outstanding would be £110.52 (rounding to the nearest 1p). This may not seem much, but with a £100,000 loan (mortgage) at 7% per annum, the "error" after 1 year is £250.
No, banks usually (in fact almost certainly always) use simple interest when calculating how much interest to apply to the account. Compounding is merely a side-effect of applying interest more frequently than once a year, and does not mean they "use compound interest".
Indeed.
Not so. This would only be correct if interest were applied (i.e. actually charged) to the account every day, but that is not usually done even when they say interest is "calculated" daily.
To expand on your example, if interest is applied only once a year, but calculated daily, then every day will generate an interest charge of about 2.74p, and at the end of the year they're all added together and 365*2.74p = £10.00 is added to the account.
On the other hand, if interest is applied quarterly, then 92*2.74 (£2.52) would be applied at the end of the 1st quarter. Each day of the 2nd quarter would generate 2.81p interest and so 91x2.81p (£2.56) would be applied at its end, and at the end of the 3rd and
4th quarters, respectively, 91x2.88p (£2.62) and 91x2.95p (£2.69) would be added, leaving a balance of £110.38. This extra 38p results from the quarterly compounding, and if compounding monthly it would be 47p, if weekly 51p, and if daily 52p (as you pointed out).
It's important not to infer "compounded daily" from "calculated daily". Daily calculation simply means that intra-period balance variations (such as from repayments) are taken into account when calculating any period's interest charge.
Where do you get that from? The reality is that money grows exponentially, ie the amount of interest you earn is proportional to the amount of money in the account. Simple interest rates are OK if the period of the investment is fixed. But where period is not fixed interest will always be highest on the shortest period.
So however bank charges interest to customers they will be using compound rates to model interest internally.
Actually it is so. Day count conventions such as ACT/360 are a method of converting days into a year fraction. If the year is 365 and the rate is
10% simple annual the interest charge would be 10.52.
You seem to be missing the point of calculating the rate for a day as
1/360 the rate for the year.
If you use any compound rate it does not matter how often you apply interest the overall figure should be the same. That is why we use compound rates rather than simple rates, they are consistent for different time periods. This is true regardless of the way the compounding is quoted. Daily or annual compounding is just like measuring in pounds or kilos.
The only thing Graham seems to be confused about is that a day count convention of ACT/360 implies simple interest rates, it does not. However it is true that ACT/360 is most often used with simple interest rates.
Standard Banking practice. I told him about 10 years ago.
. Thats right, but at the correct compounding period, not daily.
No it isnt.
Thats right, because in the example you are using you are compounding at a more frequent interval than the interest is actually compounding at. You are confusing present values etc., with interest compounding.
But banks use 365 days in their calcs.
Thats right, because the term 'compound rate' is the effective rate, not the nominal or simple rate which is actually used.
Thats is why banks also show AERs and APRs.
I think you are confusing rates of nominal interest that are expressed on an annual basis and the effect of that rate being compounded.
Standard Banking practice. Well I work for a bank admittedly in interest rate derivatives not high street banking but I'm not aware of this Standard Banking practice. Where can I get hold of a document detailing the practice.
I thought that the banks were allowed to do things pretty much as they pleased, within limits of course.
You mean in the same way it is "correct" to measure in kilometers and not miles? The rate of compounding will not affect internal calculations any more than choosing to measure in kilos or pounds would.
It is important to make clear to the customer the compounding frequency, but by default I would expect a compound rate to be annual compounding.
Yes I wasn't really reading what he actually said. I think he probably meant to say what I said below.
No this example I gave has no compounding, it just shows how the banks can charge a few days extra interest by using a funny way of converting days into years. This method of calculating year fractions from days is called a Day Count Convention and is independent of the compounding frequency.
Do they for mortgages? Where is this specified?
APR is something different it includes fees etc. I guess AER is an approximation of the interest charges quoted as an annually compounding rate? Does it have an exact definition?
If a compound rate is used correctly it shouldn't matter when interest is actually applied to the account.
No. I understand the difference between simple and compound rates.
What I don't understand is the specific calculation method that Nationwide use to calculate interest on my standard repayment mortgage. If you know how Nationwide do this calculation I would love to know what it is.
As I said I tried to reverse engineer it but couldn't come up with anything sensible.
If I assume that the quoted rate (BMR = base mortgage rate) is a simple rate with interest applied monthly, day count ACT/365, then the interest charged on my statement is lower than my calculation by about 1%. If I assume that the BMR is an annually compounding interest rate, using a day count convention of ACT/360, and that interest on payments has effect the day after statement date then the interest charged on the statement is about 0.1% higher than this calculation.
Now I'm not saying this proves anything all I'm saying is that like the OP I would like to know how this calculation is actually done, so that I can reproduce it to the penny.
Economics. And still in the process of getting it. I am professionally dealing with uncertainty (statistics), maybe that's the problem.
I am currently looking at the most simple case possible - calculating the interest for the initial month of the mortgage. I looked at four methods of calculating it: day counts of 360 or 365, and daily compounding or not. None of these, when calculated with an integer number of days (I tried 29, 30, 31 or 32), leads to the figure stated by Nationwide. Some are lower, some are higher.
I might do (or get my boyfriend to do it, since I am not on the mortgage). I'll report back when I get a reply.
When I've written it I'll let you know. Why not trot downstairs the retail banking department and ask them?
Yes, thats right. But in this regard I think you will find that they all do it as I describe, for mainstream lending that is.
Would you? What about the quarterly interest applied by most banks on mainstream lending? What about rolling over LIBOR periods shorter than 1 years?
Thats isnt why you ended up with 10.52, you ended up with that because you compounded daily. If it were compounded annually, as you suggest above, then it would be 10.
By their use of the word 'daily'.
I know but in a fee free loan it is good enough for the purpose of my example.
Thats right,
Yes, I will post the answer later. Its in the BBA site somewhere.
You are merely looking at it the other way round. Some lenders quote the simple annual rate and also the AER. Others, such as ING just quote the AER. This ended up with those taking their interest monthly getting less than they thought.
It will depend if you have a new or an old style one I think. You may be on the old annual rest way.
Did you start with the APR? or did you assume that the quoted simple rate was the compounded rate?
Which Nationwide 'deal' are you on? Do you know the product code?
The one account accrues daily and compounds monthly. Thats what it means when it says "We'll apply interest to your account once a month by adding up the interest charges for each day and debiting the total from your account.".
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