Daily interest miscalculation?

InMyDreams

Marvin_the_Martian wrote: »

Actually, if I owed £100,000 and took a payment holiday for twelve months, at a declared annual interest rate of 4.95%, I would indeed expect to have an outstanding balance of £104,950 at the end of the year no matter whether that rate was calculated quarterly, monthly, daily or by the second. That, in my perhaps incredibly naive view, is what an annual rate of 4.95% means.

Yes, it doesn't matter on how often it is *calculated* but it does matter how often it is *applied*. As soon as you *apply* the interest owed to the account, then you have a higher balance on which to start calculating. Usually with mortgages the interest is never applied as it's paid off before. I've never applied for a mortgage holiday. But I agree that it might be good practice for banks to point out the implications of having your interest applied to your account. I would have no idea whether this happens or not.

Marvin_the_Martian wrote: »

Yes, it's probably a nitpick.

But it's a very interesting point and I guess it's the principle more than anything that is worth discussing.

Marvin_the_Martian wrote: »

As I've acknowledged in a previous post it still works out better than if I were being charged a nominal rate of 4.95% on some other basis, or charged a rate of 4.95% on the initial balance for an entire year. No, I don't expect them to change their advertised rate. I acknowledge that a nominal interest rate is an accepted way of presenting a product. What I would like is for lenders to show their working - even if it's in the fine print or buried in the handbook. They do this well enough in the case of the fees they charge, but not the interest, it seems.

I have often thought that it would be nice to be able to look up (for any product, saving or borrowing) the actual %age they use to calculate the interest daily (or however often it is calculated.... even annual paying accounts will calculate daily). But I fear that that would cause more confusion to most than current standard measures. At least the system as we have it is consistent across banks and therefore easier to compare for most. And a daily interest rate wouldn't mean anything to many people. And if it does mean anything to someone then they can probably work it out for themselves.

danm

Marvin_the_Martian wrote: »

Actually, if I owed £100,000 and took a payment holiday for twelve months, at a declared annual interest rate of 4.95%, I would indeed expect to have an outstanding balance of £104,950 at the end of the year no matter whether that rate was calculated quarterly, monthly, daily or by the second. That, in my perhaps incredibly naive view, is what an annual interest rate of 4.95% means: the rules of mathematics don't change depending on the type of product you're talking about.

Yes, it's probably a nitpick. As I've acknowledged in a previous post it still works out better than if I were being charged a nominal rate of 4.95% on some other basis, or charged a rate of 4.95% on the initial balance for an entire year. No, I don't expect them to change their advertised rate. I acknowledge that a nominal interest rate is an accepted way of presenting a product. What I would like is for lenders to show their working - even if it's in the fine print or buried in the handbook. They do this well enough in the case of the fees they charge, but not the interest, it seems.

most of them do explain their workings in the mortgage T&C's.

Its been a long time since last night, and i've forgotten the oiginal arguement, but im still not sure i undestand your concern here.

To break it down into it most simple form.

I have an interest only £100 mortgage and the interest rate advertised by the lender is 12%.

I pay my mortgage monthly, and interest is calculated as per the terms and conditions.

If it is monthly, the lender will take the outstanding mortgage balance at a set date in the month (always £100 in this case sa its an IO mortgage) and do the following calculation. - £100*(12%/12) = £1. They collect this by DD from your account At the end of the year you have paid £12

It is is daily, they do the calculation of £100*(12%/365) = 3.28p. Each month, they collect the amount owed from your account by DD, and at the end of the year you have paid £12

If yearly, at the start of the year, they calculate £100*12% = £12. they then divide this into 12 equal instalements of £1 and collect this by DD each month. At the end of the the year you ahve paid £12.

Its that simple. The only thing that differs is the APR. This takes into acccount fees, time value of money etc. but is irrelevant for this discussion

[Deleted User]

danm wrote: »

no you wouldn't, as the mortgage balance (principal + outstanding interest) in month 2 is higher, so you would pay more interest in the second month. (obviously this may differ between lenders).

This is comparing apples with oranges. Paying more interest because the balance is higher is not the same as applying a higher interest rate.

From your Wiki, the only bit to worry about, is the small part on 'Simple Interest'. Nominal rates/efffective rates are not relevant.

If the headline rate is all one has to work with, whether it is a nominal or effective rate is highly relevant in terms of calculating how much one actually owes at any given time. If I didn't have access to online banking, in order to work out what my daily interest was, I would have needed to know whether the rate advertised was a nominal rate or an effective rate.

The 'headline' rate and the APR are all that matters with mortgages

Headline rates are not all they're cracked up to be unless you know how that rate is actually applied, and that depends on the product. As I thought we'd established, not all values of "4.95% interest rate" are the same. APRs are equally unhelpful if the assumptions made in APR calculations don't apply to you - for instance, if you make use of a product's flexible features. They may also be unhelpful if things like arrangement fees aren't included (and as we've discovered lately on approaching the end of our fixed period, some of the arrangement fees out there at the moment are truly shocking).

InMyDreams

danm wrote: »

but im still not sure i undestand your concern here.

I think I understand Marvin's concern. Nitpicking or not, it's frustrating when numbers don't seem to add up as you expect. All your examples (danm) work (as they should) because the interest is never applied to the account. If (as would be the case as with payment holidays) the interest was to be applied to the account during the year, the the overall interest at the end of the year, *based on the original balance* would in 'effect' be higher as you are notionally basing it on the starting balance (which was the true balance only for the first month). This is why Marvin would have an outstanding balance of greater than £104,950 on his £100K mortgage.

(And I did that without making a savings analogy once )

Ps... ok, Marvin got there first... maybe I got my understanding of his concern wrong... sorry!

[Deleted User]

InMyDreams, I hope you don't mind if I condense both replies into a single post.

InMyDreams wrote: »

But it would only be 'effective' to those people not paying off their interest which will be a very small minority. The 'actual' interest rate is the one they advertise and the one you pay over the year, whether on repayment or interest only. This is what you pay on whatever balance is outstanding.

There appears to be some contention between this paragraph and the one below, or maybe that's just my interpretation of it...?

Whether you are on repayment or interest only makes no difference to the rate of interest. You pay on what is outstanding. If you are on repayment, that balance goes down each month so you pay less (in interest), but you are still paying the same rate.

I agree completely with this paragraph. If you follow that reasoning to its logical conclusion, though, if you don't pay back any of the money at all, you are still paying the same rate. And here's where we get back to my point of principle: I personally think that an annual interest rate ought to give the same result after one year's interest accrued on an initial loan, before payments are taken into account. Heck, maybe it is just me.

???? *Everyone* pays a repayment mortgage like that.

Not really, because no-one on a repayment mortgage pays just the interest; by your reasoning, a bank could actually argue for a lower headline interest rate than that already published, on the grounds that you haven't actually paid the full interest on all of the initial capital by the end of the year (because you've paid off some of the capital). I'd suggest that this way lies madness

InMyDreams wrote: »

Yes, it doesn't matter on how often it is *calculated* but it does matter how often it is *applied*.

Of course, I recognize that the amount one pays, the number of actual interest periods in that year and the points at which interest is recalculated all affect how much interest one will pay in practice. But that's also why I'd like more clarity - particularly as we're approaching that time again where we must step once more into the minefield of comparing mortgage products, which is not made easier if one has to guess at how they're calculating their interest charges.

But it's a very interesting point and I guess it's the principle more than anything that is worth discussing.

I'm glad someone else thought so.

I have often thought that it would be nice to be able to look up (for any product, saving or borrowing) the actual %age they use to calculate the interest daily (or however often it is calculated.... even annual paying accounts will calculate daily). But I fear that that would cause more confusion to most than current standard measures. At least the system as we have it is consistent across banks and therefore easier to compare for most. And a daily interest rate wouldn't mean anything to many people. And if it does mean anything to someone then they can probably work it out for themselves.

I think that a line saying "we apply interest daily at a rate of 1/365 of the nominal interest rate" in the handbook (and on the Web site) would be quite sufficient. That way, the information is available in case anyone cares to work it out for themselves. (Though interestingly, I don't know whether they still do it but the Student Loans Company did actually publish the - daily, or monthly? - interest rate on their statements.)

danm

Marvin_the_Martian wrote: »

I personally think that an annual interest rate ought to give the same result after one year's interest accrued on an initial loan, before payments are taken into account. Heck, maybe it is just me.

now i understand your issue. It's taken me a while:rolleyes: .....but the more i think about it, the more i think it is just you .

[Deleted User]

danm wrote: »

most of them do explain their workings in the mortgage T&C's.

I have to confess that in my case I couldn't find it in the handbook. If I had, I wouldn't have posted this thread. And in any case, I'd argue that this information shouldn't just be available in the T&Cs, but in the sales brochure or on the Web page, even if it's in small print or on a separate FAQ page saying "how we calculate interest on our daily interest rate products". I would expect to see how they calculate the rate itself (e.g. headline rate divided by 365), under what circumstances it is recalculated (e.g. whether the amount charged is recalculated every day, or at the beginning of the month, or when a payment clears) and when it is applied (e.g. interest applied the following day on the previous day's balance). Now some of this information is readily available, but not all of it in all cases.

There is a serious point to all this, though: as a matter of principle, if I go shopping for mortgage products, I ought to be able to see exactly what's on the table, and not have to rely on a financial advisor's esoteric knowledge of any particular brand of products in order to get the information I need. And all this information is relevant if I'm to be able to work out how much a product will cost based on my personal circumstances and budget, not based on hidden or irrelevant assumptions that I will pay X amount a month over a period of Y years.

Crucially, in my case the first item of information I've listed here wasn't available - which is why, going back to my OP, I made the obviously-daft-to-all-but-me assumption that compound interest meant exactly that, based my calculations on a daily interest rate of (1 + 4.95% ^ (1/365)) - 1 (as opposed to the rate of 4.95%/365).

Its been a long time since last night, and i've forgotten the oiginal arguement, but im still not sure i undestand your concern here.

My concern is a lack of clarity regarding how interest on the product is calculated.

I still maintain that APRs and headline rates are not all they're cracked up to be. Of what relevance to me is an advertised APR of, say, 6%, if it's based on the assumption that I'll keep the product over a 25-year period and never overpay, if I intend to pay it off in six, or switch to another product after three? Of what relevance is a headline rate of 5% if product A and product B (both with headline rates of 5%) end up charging me different amounts of interest because they're applied differently?

To break it down into it most simple form.

I have an interest only £100 mortgage and the interest rate advertised by the lender is 12%.

I pay my mortgage monthly, and interest is calculated as per the terms and conditions.

If it is monthly, the lender will take the outstanding mortgage balance at a set date in the month (always £100 in this case sa its an IO mortgage) and do the following calculation. - £100*(12%/12) = £1. They collect this by DD from your account At the end of the year you have paid £12

It is is daily, they do the calculation of £100*(12%/365) = 3.28p. Each month, they collect the amount owed from your account by DD, and at the end of the year you have paid £12

If yearly, at the start of the year, they calculate £100*12% = £12. they then divide this into 12 equal instalements of £1 and collect this by DD each month. At the end of the the year you ahve paid £12.

Its that simple. The only thing that differs is the APR. This takes into acccount fees, time value of money etc. but is irrelevant for this discussion

I fear we've gone back round in circles. You're comparing apples with oranges, as you're basing your argument on the assumption that paying 3.28p a day from day one is equivalent to paying £12 at the end of the year. Clearly this is a false assumption.

[Deleted User]

danm wrote: »

most of them do explain their workings in the mortgage T&C's.

I have to confess that in my case I couldn't find it in the handbook. If I had, I wouldn't have posted this thread. And in any case, I'd argue that this information shouldn't just be available in the T&Cs, but in the sales brochure or on the Web page, even if it's in small print or on a separate FAQ page saying "how we calculate interest on our daily interest rate products". I would expect to see how they calculate the rate itself (e.g. headline rate divided by 365), under what circumstances it is recalculated (e.g. whether the amount charged is recalculated every day, or at the beginning of the month, or when a payment clears) and when it is applied (e.g. interest applied the following day on the previous day's balance). Now some of this information is readily available, but not all of it in all cases.

Crucially, in my case the first item of information I've listed here wasn't available - which is why, going back to my OP, I made the obviously-daft-to-all-but-me assumption that compound interest meant exactly that, based my calculations on a daily interest rate of (1 + 4.95% ^ (1/365)) - 1 (as opposed to the rate of 4.95%/365).

Its been a long time since last night, and i've forgotten the oiginal arguement, but im still not sure i undestand your concern here.

My concern is a lack of clarity regarding how interest on the product is calculated.

To break it down into it most simple form.

I have an interest only £100 mortgage and the interest rate advertised by the lender is 12%.

I pay my mortgage monthly, and interest is calculated as per the terms and conditions.

If it is monthly, the lender will take the outstanding mortgage balance at a set date in the month (always £100 in this case sa its an IO mortgage) and do the following calculation. - £100*(12%/12) = £1. They collect this by DD from your account At the end of the year you have paid £12

It is is daily, they do the calculation of £100*(12%/365) = 3.28p. Each month, they collect the amount owed from your account by DD, and at the end of the year you have paid £12

If yearly, at the start of the year, they calculate £100*12% = £12. they then divide this into 12 equal instalements of £1 and collect this by DD each month. At the end of the the year you ahve paid £12.

Its that simple. The only thing that differs is the APR. This takes into acccount fees, time value of money etc. but is irrelevant for this discussion

I fear we've gone back round in circles. You're comparing apples with oranges, as you're basing your argument on the assumption that paying 3.28p a day from day one is equivalent to paying £12 at the end of the year. Clearly this is a false assumption.

InMyDreams

Marvin_the_Martian wrote: »

InMyDreams, I hope you don't mind if I condense both replies into a single post.

Be my guest

Marvin_the_Martian wrote: »

There appears to be some contention between this paragraph and the one below, or maybe that's just my interpretation of it...?

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. [Edit: the total payment obviously stays the same because the capital part increases as the interest decreases]. 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.

Marvin_the_Martian wrote: »

I agree completely with this paragraph. If you follow that reasoning to its logical conclusion, though, if you don't pay back any of the money at all, you are still paying the same rate. And here's where we get back to my point of principle: I personally think that an annual interest rate ought to give the same result after one year's interest accrued on an initial loan, before payments are taken into account. Heck, maybe it is just me.

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?

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

Marvin_the_Martian wrote: »

Not really, because no-one on a repayment mortgage pays just the interest; by your reasoning, a bank could actually argue for a lower headline interest rate than that already published, on the grounds that you haven't actually paid the full interest on all of the initial capital by the end of the year (because you've paid off some of the capital). I'd suggest that this way lies madness

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

Marvin_the_Martian wrote: »

Of course, I recognize that the amount one pays, the number of actual interest periods in that year and the points at which interest is recalculated all affect how much interest one will pay in practice. But that's also why I'd like more clarity - particularly as we're approaching that time again where we must step once more into the minefield of comparing mortgage products, which is not made easier if one has to guess at how they're calculating their interest charges.

I don't think you have to guess... if they are calculating daily then they are all using the same calculation, aren't they? You don't need to work out a daily interest rate to compare mortgages. Now if some did it your way and some did it the standard way, that would indeed cause much confusion!

Marvin_the_Martian wrote: »

I'm glad someone else thought so.

I think that a line saying "we apply interest daily at a rate of 1/365 of the nominal interest rate" in the handbook (and on the Web site) would be quite sufficient. That way, the information is available in case anyone cares to work it out for themselves. (Though interestingly, I don't know whether they still do it but the Student Loans Company did actually publish the - daily, or monthly? - interest rate on their statements.)

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

danm

Marvin_the_Martian wrote: »

I fear we've gone back round in circles. You're comparing apples with oranges, as you're basing your argument on the assumption that paying 3.28p a day from day one is equivalent to paying £12 at the end of the year. Clearly this is a false assumption.

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

(Unless you are talking about the time value of the payments, but this would be accounted for in an APR calculation)