simple or compound interest?

engineertony

Hi John,

To apreciate this we need to see it from the other side. Can you imagine investing in a bank at 5.49% per annum and you the tell them to work out the interest at 5.49/12% per month and add it to yor balance. Then the next month another 5.49/12% and so on.

At the end of one year you would find your capital increased by 5.63%

The FCA regulations simply state that the APR takes fees into account it says nothing about strange ways of calculating interest. It does say that any significant features should be pointed out and examples given.

I don't think banks and credit card companies have the same problem or else there would be a continuous argument about "true" or "fiddled" rates of interest.

John1993_2

engineertony wrote: »

Hi John,

To apreciate this we need to see it from the other side. Can you imagine investing in a bank at 5.49% per annum and you the tell them to work out the interest at 5.49/12% per month and add it to yor balance. Then the next month another 5.49/12% and so on.

As long as I knew on which basis the rate was being quoted, the headline figure is completely irrelevant. If I invested for a year at 12% simple interest, or at 11.387% paid monthly and reinvested, then I'd end up with an identical amount at the end of the year.

These are not "strange" ways of calculating interest, they are simply diffferent but perfectly conventional ways of expressing the same thing.

Your problem seems to be that you thought you were being quoted on one basis, while you were actually quoted on another.

Again, where do you get the idea from that one way of quoting interest is "true", and one is "a fiddle". In my example above, which is the true rate, and which is the dishonest one, and why do you think this?

And edited to add, as I said above, I trade these things, which means I bot hbuy and sell, so am on both sides at variouus times. IIt makes no sense to say that I need to view it from one "side" or the other. The diiscussion does not require stepping into somoene else's shoes.

bigadaj

I can see why there is a query and how different rates can be quoted. Do you know if your mortgage is subject to daily, annual or monthly interest, if its annual then the lender is correct in his calculations, if the others then you are correct to a greater or lesser extent.

engineertony

Hi John,
Good to get an insider’s point of view.

I find it strange to say the headline figure is irrelevant. If you invested 100,000 at a 12% headline figure and got only 10% because the headline figure was irrelevant I don’t think you would be happy. Of course it is relevant, it’s all we borrowers have, apart from an APR “for comparison purposes” which is said to include up front fees.

If I leave my money in the bank at 10% p.a. then I expect to have 10% more at the end of one year, I don’t want to be told that the figure was completely irrelevant.

If you invested for a year at 12% as you say, and you have 12% more at the end of the year, then all is well and good. If you make additional deposits or withdrawals during the year then it gets more complicated. A rate must be reached which maintains your 12% per annum and that costs the borrower 12% per annum. On a monthly basis this is 0.9489 % which multiplied by 12 gives your figure of 11.387%, which is not an annual rate, but merely a figure found by multiplying the monthly rate of 0.9489 by 12. This figure of 0.9489% is the figure which when compounded gives 12%, i.e. 1.009489^12=1.12

Which is true? You are missing the third case which is 12% divided by 12 which is 1%. This is the case I am discussing on this thread. A lender quotes a rate of 12% and then applies it at 12 /12 % i.e. at 1% per month giving something in the region of 12.68%.

This started as me querying the monthly payment by Virgin Money but now I am realising that the building societies are employing a number of methods in calculating interest and credit for payments, which always result in a figure of interest paid at the end of a 12 month period which is greater than the “agreed” or “true” or “morally correct” or “honest” or “just” or whatever you prefer to call it. The borrower is always the loser.

This is peculiar to building societies as banks and other financial institution have money going to and fro and have to agree on a daily rate which is agreeable to both sides. In my limited checking I find that the rate is calculated from the annual rate as I've already described. This rate is compounded to give the quoted annual rate. It would be uncceptable for one bank to tell another that the quoted rate was completely irrelevant.

@bigadaj

As above a simple interest case is easy, wait 12 months and collect your interest.
When money is going in as payments or out as withdrawals then a rate has to be found which maintains the agreed annual rate. The building societies considered so far use a daily rate and a monthly rate which doesn't agree with the yearly rate. In one case above they are charging interest on money that has already been paid back.
There is a clear and established way of doing business in such cases which is used by the banks and credit card companies which is a daily rate which compounds to the agreed annual rate. For some reason the building societies are not doing this, but are using combinations of simple and compound interest, as well as using a capital balance as the basis for a year when the balance has decreased, in other words they charge interest on money which the borrower has paid off.

TrickyDicky101

TrickyDicky101 wrote: »

I'm looking at my 'further advance' portion of my mortgage which was taken out for £87,561 in July 2011 (this is via NW's internet banking service - which is awful in comparison to other ones I use, but that's bye the bye).

The outstanding balance at 1st Jan 2013 was £84,601.30.

The next line quotes interest payable for the year (why it is a whole year's worth I have no idea), and this appears to be charged on the days elapsed in 2013 to the 'as at' date (in this case 31st Jul 2013).

So:

£84,601.30 * 4.54% * 212/365

=£2,230.88 (NW actually quotes £2,230.92 - no idea why £0.04p difference)

As you say, this is on a 'simple interest' basis as no account is taken of intervening capital repayments.

There then follows 6 mortgage repayments of £491.18 and one in April 2013 of £647.41 to leave a balance outstanding at 31st Jul 2013 of £83,237.73.

This certainly would appear to imply their interest is charged on an initial outstanding balance basis, taking no account of capital repayments within the year.

(Incidentally, they also quote under "Interest Rate History" that my rate for my Capital Repayment Mortgage is 4.59% when this is incorrect as it is actually 4.54% (and the interest charged has been calculated on 4.54%). No idea the reason for this difference - I mention this for information only)

So, the above would suggest NW are pulling a fast one (not really charging daily interest on outstanding balance) and yet looking in the overpayments section of online banking the following is quoted:

"If you overpay by less than £500, the balance of your mortgage will reduce and you will be charged interest on the lower balance from the following day"

which suggests that overpayments are indeed reflected in the interest charged!

I must admit I am now thoroughly confused as to how NW calculates its interest. I am going to set up a spreadsheet with opening mortgage amount and monthly payments and calculate long hand what I think the interest/capital repayments should equate to.

There is inconsistency at the least in what NW is quoting via their internet banking service and the terms they quote. I look forward to identifying exactly what does apply.

OK, I pulled out my original mortgage documentation and created a long form spreadsheet to analyse interest charged and outstanding balance month by month.

First thing of note: I was incorrect in that my mortgage rate is definitely 4.59%. What can I say - age has killed off too many essential brain cells!

This is 4.59% quoted on an Actual 365 basis with monthly compounding (for those that want to know).

Anyway, the mortgage of £87,561.00 was advanced on 15th July 2011 with repayments set at £491.18 for 5 years (this is the same amount Excel will return if you use the PMT function on the advanced amount for 300 months (ie full 25 year term) at the quoted interest rate with repayments in arrears).

The long and the short is I am in complete agreement (to the penny) with NW's mortgage statement for 2011 with balance o/s as at 31/12/2011 of £86,767.65.

Fast forward another year and NW quote balance o/s at 31/12/2012 of £84,601.30. I disagree slightly here as I made it £84,612.60 (which does look suspiciously like 1 day's interest to me so maybe we are using different end points. I'm not worried about this enough to persevere looking at it, and it's in my favour anyway!).

My conclusion is, irrespective of what NW are quoting on their internet banking (which still looks somewhat wrong to me), they are actually calculating the interest and amounts o/s correctly (or close enough that I simply don't care for the insignificant differences) and sending me annual statements in agreement with my own calculations.

Panic over for me.

opinions4u

Fast forward another year and NW quote balance o/s at 31/12/2012 of £84,601.30. I disagree slightly here as I made it £84,612.60 (which does look suspiciously like 1 day's interest to me so maybe we are using different end points. I'm not worried about this enough to persevere looking at it, and it's in my favour anyway!).

Leap year?

TrickyDicky101

opinions4u wrote: »

Leap year?

I don't think it is because I was using exact days between repayment dates to calculate the interest suffered so I do not *believe* it should cause a difference.

One of the most interesting things I identified was that NW appears to have determined the repayment amounts on a repayments in arrears basis despite them quoting repayments in advance (and thus the need for interest from the point of mortgage inception to the end of the month of mortgage advance which can almost double your first repayment depending on the exact date you take out the mortgage).

It seems ... inconsistent (but ultimately doesn't cost the borrower any more money other than perhaps causing an initial cash flow problem if the borrower has not understood properly what the first repayment will be - this certainly happened to me with my first mortgage from them back in 2005. It was painful at the time).

fiesta04

Thank you TD101. Explained as it is.

That is exactly how I see my mortgage worked. I have had 3 different mortgages plus a further advance and they all worked this way.

F4