simple or compound interest?

engineertony

Hi Imma,
You've got it.

They don't have a yearly account at all. They charge interest at 5.49/12 % on my balance each month and arrive at a new balance.
The next month they do the same, charging interest on the new balance at 5.49/12%.

This is a continuous monthly procedure, and I get a four month summary, three times a year. There is no annal period where they stop and say this is the annual total, no annual balance, total interest or payments.

To everyone else...this is well worth checking in each case and come onto this site with the methods of calcualtion used by various societies, they cannot all be right and acceptable.

By banking and credit card standards, the correct rate is given by (1.0549)^0.08333
i.e. 1+ 5.49/100 to the power of one twelfth

This is the rate which when compounded over twelve months gives 5.49%.

@Jake, start revising the maths of percentages, interest rates, simple and compound interest. There's no algebra, trigonometry, or geometry, it's just arithmetic. Seriously it might be worth looking into, the PPI claims started slowly as many other scandals. They do try to get rid of complaints with various fobbing off letters and threats, and try to hide amongst the complex mathematical methods.
Most societies never tell the borrower where the figures have come from, just a statement...interest £x

engineertony

Hi Imma,

Yes you have it correct.

In my case they do not have a annual statement but they have a continuously rolling balance which is charged at 5.49/12 each month, creating a new balance.

In your examples the second case is similar, where 5.49/365 would be used to calculate a new balance. This is the amount used to calculate the next days interest. That is the simple interest rate is calculated and then used in a compound interest calculation.

Check when Nationwide make their starting point and end point. OK they start with 100,000 and add a daily interest charge of 5.49/365 % to the balance and over 365 days you have been charged a total of 5.49% of the original £100,000.
Looks OK.
In fact you only owe 5.49% at the end of the year, why did they take £15.041 on the first day after you got the loan. In fact you didn't owe them £100,000 at that point,but £99,984.959, yet they charge you based on £100,000.
This is complicated by payments received and the only true and fair way is as the banks and credit card companies do. You are charged at a daily rate which when compounded over 12 months gives the quoted rate of interest.
Mathematically it is (1.0549)^(1/365)
That is 1.0549 to the power one three hundred and sixty fifth.
This figure when compounded 365 times gives 1.0549

Looks like banks and credit card companies both for investors and borrowers are using one system which is absolutely clear and transparent and the building societies are using a fiddling system which gives them a financial advantage.

engineertony

Hi All,

The first stage of the Financial Ombudsman Service is past and I am in the hands of an "expert", who called me a few days ago to discuss this. The fact that he didn't dismiss it immediately gives me some hope.

For those following the maths, I will calculate the true rate of interest in the case above where a fixed 1/365th of the annual rate is added daily. In the case of Virgin Money they do face this discrepancy and they credit the payments at a daily rate of 1/365th of 5.49% until the end of the month where the monthly interest is charged. In fact on an annual rate of 5.49% they should credit payments for the part of one year when the annual summary is made noy to the end of the month.

Virgin have lost the annual period in the smoke and mirrors by presenting a four monthly summary to borrowers and for sure the bottom line of these statements is used as the opening balance for the next period. This way there is never a point where an annual balance can be taken as a basis for monthly fixed payments as givn by Imma Number above.

I suspect that their answer will be that 5.49% is only a guide or nominal figure and the true rate is 5.63%. To this I will reply that they are obliged to have told me this many years ago.

engineertony

Hi Imma,

There are two separate issues here.

1. If the lender maintains a twelve month interval and re-calculates this every twelve months then there is a point in time when the borrower can find a summary of whether the total payment of interest is correct. In my case 5.49%. Looks like Nationwide take the annual total amount and divide it by 365, then take this over a period of twelve months using simple interest as you say. Virgin Money however have no yearly summary, they give a statement three times per year which shows 5.49%/12 added to the balance at the end of each month. This is compound interest.

2. The other issue is credit for payments received. If I borrow £100 over 12 months at 20% per annum and pay £10 per month then although I have paid £120 which is 20% more than the original £100 it is wrong because I havent borrowed £100 for 12 months. I should not be charged 20/12% of £100 each month to sum up to 20%. As I have said earlier I haven't borrowed £100 for 12 months, after the first month I owe less than £100.

Virgin do recognise credit for payments received and credit 5.49%/365 per day until the end of the month when payment is received. This again is wrong as it should be until the end of the year for which interest is being charged at 5.49% per annum. The whole affair is dependent on an annual date when the account is updated, if this date is lost by accounting every 4 months then an error comes in which of course is in favour of the lender Virgin Money.

Interestingly, why do NW update your account daily at 1/365th of the annual rate? What capital do they use as a base for this? Is it the balance at the end of the previous year? if so then you are not paying interest on wht you owe them at a point in time but on an amount which you owed last year which is larger normally because you have paid some off.
I would love to hear from others to see how these fiddles work, always in favour of the lender.

There is only one true and honest method, that is a daily rate charged to your account which compounds to the correct annual rate. This is used by banks and credit card companies and in every case I have checked it gives the correct yearly rate when compounded over 365 days.

TrickyDicky101

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.

engineertony

Hi Tricky,

Brilliant!
They are pulling a fast one and 99% of the population cannot seeit or even begin to understand it.

I've just got the first round from the Financial Ombudsman with the reply from Virgin Money claiming it's all above board and in line with terms and conditions. He's siding with big business and claims to have investigated in a week. It takes more than a week to grasp it completely, but they have sent a detailled statement showing only when payments are received and interest is added.

I'm just digesting but at first glance it shows 5.49/12 % added to the balance each month, and a new balance is stated which is then used the following month....this is compound interest.
At the same time they show a few pence credit for payments received at the end of each month, when in fact payments should be credited for the whole accounting period or proportion of one year.

It's much as I thought & expected from the FOS, aligned generally with big business, but I have until 14 August to challenge, which of course I will.

As I've stated above many times there is only one fair and honest method, that is to calculate on a daily basis at an interest which compounds to 5.49% per annum. If this is done then every borrower will find himself better off.

Your case shows the fiddle very well....
You are paying interest on money you have already paid back in payments. At the same time they are claiming to be charging daily interest.

amnblog

Dear EngineerTony

In your business you may be used to working within a few thousandths of an inch.

That is not good to us in this business - the FCA say we brokers have to be spot on.

engineertony

Hi Amnblog,

Not too sure what you are saying here.

The discussion is about whether a borrower should pay interest on money he has already paid off, that's really the bottom line.

Seriously if you can make a positive contribution to this discussion I would apreciate it. It appears that different building societies have various ways of calculating what the customer pays in interest and it always shows a small error in their favour, when banks and other financial institutions use a true daily rate.

There is a formula in the MCOB FCA reglations but it's difficult to follow. The interest compounded over 365 days should result in the quoted annual rate that the lender claims to be charging.

If x% is the daily rate and y% is the yearly rate then:
(1+ x/100)^365 = 1+y
i.e. 1+x/100 multiplied by itself 365 times equals 1+y

In my case an annual rate of 5.49% is the same as a daily rate of 0.0146%
That is (1.000146)^365= 1.0549

The last line is per unit not per cent, electrical engineers use per unit rather than per cent but it's all the same mathematically.

John1993_2

engineertony wrote: »

For those following the maths, I will calculate the true rate of interest in the case above

There is no one "true" rate of interest. The same cashflows can be expressed as a whole range of different interest rates depending on what interest rate basiis you are using.

APR is one rate, but it's no more "true" than a rate quoted based on compounding monthly, daily, hourly, continuously, or even three-weekly (if you wanted something so unusual).

It looks as though you've been quoted an annuall rate, which is to be compounded monthly. There's nothing wrong with this, it's just different to the APR. As long as you were also told the APR then no-one's done anything wrong.

John1993_2

engineertony wrote: »

I would love to hear from others to see how these fiddles work, always in favour of the lender.

They aren't "fiddles" I trade interest rates for a living, and will happpily quote all day long on compounded, averaged, weighted averaged, compounded at base plus a spread, adjusted, nonasdjusted, annual money, semi-bond, or any other basis you want for a swap or a loan. In every case, the deal will end up wit teh same net vaue to me, but in each case the quoted interest rate is different.

You seem to be assuming that there is only one "right" way to quote an interest rate. This isn't the case, much as you might hope that it is.

I am perfectly able to quote you a rate of "6%, compounded monthly". This means that each month you pay about half a percent in interest. Compound that up, and you get an APR of 6.17%. Neither is more fundamental, or more "true".

Edited to add, there is no "correct" way to decide when to take account of payments made, either. You can quote a flat rate of interest if you want (as car dealers are wont to do), which gives no credit for payments until the end of the loan. If you do this them the interest rate is quoted with a much smaller number, as the interest is applied to the starting balance for the life of the deal.

I could show you two loans, with identical cashflows (and so exactly as expensive / cheap as each other), and describe one as a flat rate of 6%, ad the other as an APR of (about) 12%. Each one is identical value, each is as good as the other. You seem to be implying that the "6% flat" deal is unfair.