Daily interest miscalculation?

[Deleted User]

InMyDreams wrote: »

I don't see the contention Whether on IO or repayment, you pay off your interest in full each month before it is applied to the account. If on repayment, you also pay an extra amount to chip away at the capital. The rate of interest applied does not change, although the amount will because for IO it stays the same and for repayment it gradually reduces. The amount that is, not the rate.

I think we're both agreed that the rate does not change depending on how much one repays.

The 'effect' of paying an apparently higher rate is only evident for those not paying off their interest. The case of a payment holiday is the only example I can think of. Those on repayment are still paying off their interest each month if that is what you meant.

I think danm's examples above (inadvertently) demonstrate why I do not consider this reasoning to be valid.

To take two of his examples, in Example A, one pays 3.28p interest per day for twelve months. In Example B, one pays £12 interest at the very end of the year. In both cases, the "headline rate" is 12%. Danm's example assumes that accruing interest at a rate of 3.28p from day one is equivalent to making a single payment of £12 at the very end of the year.

But it isn't. Because if in example A I didn't want to pay 3.28p from day one, but instead wanted to repay on the same basis as in example B (i.e. a single payment at the end of the year), I'd end up accruing interest not only on the initial capital but also on the interest charges themselves; so the interest I'd have to pay at the end of the year would not be £12, but around £12.74. In other words, all other things being equal, example A incurs the higher effective rate of interest.

Hmm. Look at it another way... At the end of month one, you will have interest to pay (that is how mortgages work). Think of it like a bill that you have to pay. You have to choice whether to pay this from other funds (eg your current account) or borrow it from somewhere. Taking a payment holiday effectively means that you are borrowing this interest payment from your mortgage, thus increasing it's size. If you chose to borrow more from your mortgage to pay for a car or holiday, you would expect the interest over the rest of the year to still be calculated on the original balance, before that extra borrowing was taken into account?

As far as I can tell, unless I were prepared to contribute to my mortgage on a daily basis (impractical, to say the least), it increases in size most of the time anyway.

Honestly, I *can* see what you are saying, but the maths just doesn't work like that.

??? I don't see how you reach that conclusion.

Why use a rate that would be equivalent to everyone taking payment holidays when that's not what most people are doing most of the time? That's not how mortgages are designed to work.

??? You said yourself, "The rate of interest applied does not change". If one is taking payments into account at all to justify a particular headline rate, one is negating that statement: you're implicitly saying that the interest rate does depend on payments. You can't have it both ways.

Used in the intended way, you will be paying your 4.95% interest over the year. Yes, if you are going to start trying to compare daily interest rates, you have to have a clearer idea of the maths, but lets be honest... there aren't many of us that do that

Huh???? You can't pay off any capital until you have cleared the interest charges. Or am I missing something here?

You said yourself that how much you repay has no bearing on the interest rate. So why does your argument depend on a minimum payment? This is not logical.

I don't think you have to guess... if they are calculating daily then they are all using the same calculation, aren't they?

Are they?

You don't need to work out a daily interest rate to compare mortgages.

You do if interest is being applied and compounded daily.

Now if some did it your way and some did it the standard way, that would indeed cause much confusion!

So do you think it will go down to 1/366 next year? :beer:

I have no idea!

[Deleted User]

danm wrote: »

im not sure why you feel this is a false assumption.

If I'm paying annually I don't have to pay anything at all until the end of the year. If I were to treat the product that accrued daily interest on the same basis, with a single annual payment, what would fall due - based on compound interest on the capital and all the daily interest charges - would not be £12, but around £12.74.

danm

Marvin_the_Martian wrote: »

If I'm paying annually I don't have to pay anything at all until the end of the year. If I were to treat the product that accrued daily interest on the same basis, with a single annual payment, what would fall due - based on compound interest on the capital and all the daily interest charges - would not be £12, but around £12.74.

I don't know of a mortgage where you can pay annually.

They can charge the interest to the account annually, but you would still pay monthly. I think you are maybe confusing the 'charge' of interest to the mortgage account, with the 'payment' by you, the borrower.

whether interest is charged daily or yearly, i always pay monthly, and on a IO would pay £12 either way.

going back a few messages, you seem to be stuck on the idea of compund interest and im not sure why. unless in default, mortgages are not subject to compounding.

[Deleted User]

danm wrote: »

I don't know of a mortgage where you can pay annually.

Hey, I was using your example.

They can charge the interest to the account annually, but you would still pay monthly.

Even if one pays monthly, the cumulative daily interest charges, compounded over a period of one month, would add up to slightly more than £1. (£1.0102422... to be more accurate.)

I think you are maybe confusing the 'charge' of interest to the mortgage account, with the 'payment' by you, the borrower.

I have to confess that I don't see how.

whether interest is charged daily or yearly, i always pay monthly, and on a IO would pay £12 either way.

going back a few messages, you seem to be stuck on the idea of compund interest and im not sure why. unless in default, mortgages are not subject to compounding.

Are they not? As far as I can tell from the documentation of my mortgage, interest is calculated daily on the previous day's balance. So previous interest charges are taken into account when calculating the next day's interest. Therefore, unless I pay daily - a highly impractical scenario, and one that no borrower follows - my mortgage accrues interest not only on the capital, but also on any daily interest that is applied. I'm "stuck on the idea of compound interest" because that's how it actually works.

danm

All my examples pad monthly. The total amount paid at the end of the year is always the same (£12)

which borrower are you with, i'll see if i can find the T&C's.

Interest might be calculated daily, but as it is only due to be paid by you monthly, they will not compound anything until you have missed your monthly payment.

What balance does it refer to? Principal Balance, Capital Balance, Mortgage Balance? Total Balance

[Deleted User]

danm wrote: »

All my examples pad monthly. The total amount paid at the end of the year is always the same (£12)

Only if you build in several assumptions, like paying it off on a daily basis, or not compounding the daily interest. The former is clearly not realistic, and the latter doesn't appear to be true.

which borrower are you with, i'll see if i can find the T&C's.

To follow by PM.

Interest might be calculated daily, but as it is only due to be paid by you monthly, they will not compound anything until you have missed your monthly payment.

This statement does not appear to correlate with the fact that my daily interest charge went up from £8.15 to £8.16 once the cumulative interest charges pushed the total balance above around £60,180. The only way the maths works here is if the interest were being calculated on the total outstanding balance (which includes any previous interest charges). Maybe it works differently with different lenders. I don't know. (This is according to the online banking facility, so it may or may not be accurate.)

What balance does it refer to? Principal Balance, Capital Balance, Mortgage Balance? Total Balance

It's not specific (IIRC; documents are at home). As far as I can tell it's on the total balance.

Though I suspect that the point may be moot anyway, given that we've overpaid quite substantially; even if it said "capital balance", a lender might offset the interest against the overpayments (effectively increasing the capital balance) rather than treating it separately. I have no idea.

InMyDreams

Don't have time to read through all the replies in detail at the moment. But I'm sure all the confusion lies (as danm points out) with the difference between interest *calculated* and interest *applied* (Marvin, you appear to you these terms synonymously). No, mortgages are not compounded (as I've said earlier) because the interest is never applied unless you miss a monthly payment. Only if it was applied (ie with a holiday or if you miss a payment) would there be any compounding and your notional 'effective' rate be seen.

It's the same with savings accounts (sorry, I knew I said I wouldn't mention them again). You don't earn interest on your previous day's interest. Only when it's applied to your account at the end of the month/year do you start to earn interest on it.

[Deleted User]

If, come the first of next month, the balance on my mortgage shows up something wildly different to what the online facility says it is now, then I'll hold my hands up to that. With the information I have currently, it appears as if interest is being calculated and applied on a daily basis. I'll admit that I may have misunderstood this, though. Right now, I don't think I'm really any closer to an understanding of how the product I have actually works. While maths I can handle, the arcane workings of mortgage products aren't my forte

InMyDreams

Marvin_the_Martian wrote: »

You said yourself, "The rate of interest applied does not change".

Guilty as charged . It was incorrect and confusing to have used the word 'applied' and I did exactly what I've accused you of doing! The sentence makes much more sense if you simply delete the word all together.

But I think all the other points you make are down to whether or not the interest is applied and compounded daily or not. I cannot see my mortgage online, so I've no experience of seeing how the balance moves daily. I've just looked at my annual mortgage statement though, and it is quite explicit. Each month it states the 'interest due' as a debit on the first of each month, the same date (assuming a weekday) as my payment is applied which clears it (and a bit of capital). And I've just checked the amount and it works out at exactly 1/12 of my mortgage rate. Not even adjusted for number of days in the month, so I guess the 1/366 idea is out. At least for my mortgage. And it certainly hasn't been compounding daily throughout the month. That doesn't mean it's not calculated daily.

In fact I'm able to check that because in May last year I made an overpayment in the middle of the month. At a rate of 1/31 of 1/12 of the mortgage rate each day, the interest I paid on the first of the following month works out to the penny (based on no compounding). Which it shouldn't have done actually, as a) May's payment went in on the 2nd (the 1st being a bank holiday) so was 'late' by a day and b) I used overpayment date as the day my payment was received, but according to my statement it wasn't applied until 3 days later. Both of these should have caused me to pay a little more than expected, but apparently I didn't.

Marvin_the_Martian wrote: »

If, come the first of next month, the balance on my mortgage shows up something wildly different to what the online facility says it is now, then I'll hold my hands up to that. With the information I have currently, it appears as if interest is being calculated and applied on a daily basis. I'll admit that I may have misunderstood this, though. Right now, I don't think I'm really any closer to an understanding of how the product I have actually works. While maths I can handle, the arcane workings of mortgage products aren't my forte

And if you find that you have indeed had your interest applied to the account and compounded daily, then hands up here too

Would love to play around with your figures though... happy to swap mine if you want...

WildHaggis

Just a little <hopefully helpful> aside here. Computers are stupid, nd calculate what they are told to do. Some lenders use 360 days as a 'year'. Some use 365, some use 1/12 of the annual amount every month. All are 'valid', and the APR is supposed to be a figure that is comparable... maths is a complex subject.

But, becuse computers are stupid, it is often easy to beat them - depending on the lender. If you r lender works like this :NACM (Nominal annual rate compunded monthly - lots of them do) The monthly interest calculation is done on the 'loan balance' and interest is added into the account. Pay your monthly instalment so that it reduces your balance BEFORE the monthly interest is charged. On a 100000 mortgage, paying a day or two early will knock off about 2 quid per month, and will reduce a 25 year mortgage by about two months...