simple or compound interest?

Thrugelmir

engineertony wrote: »

I lend you £100 at 12%.
At the end of the year you owe me £112.
If I charge you 1/12 of 12% per month, i.e. I take the simple interest rate and then apply it compound, then you will find you have paid around 12.68%.

£100 + 12%x£100= £112
but £100x (1.01)12= £112.68

If I take a mortgage at 5.49% then I expect to pay 5.49% not 5.64% which is what they are charging me.

Have you calculated the rate on the basis of the amount of interest you are being charged. Which will allow for the number of days within a month (or charging period). As this will vary. A simple 1/12 th calculation is to simple.

engineertony

Hi Holly,
I could see that the 1974 credit act didn't specificallt include mortgages, I thought it strange when it is fundamentally a secured loan.
Anyway I have already referred to the MCOB stuffm I was pointed there by a helpful person at the FSA. It's not a lot of help to the average householder like myself, full of cross references, and jargon needing the glossary, and the formula for APR doesn't show how the monthly payment on an interest only mortgage is calculated from the nominal rate of interest. The experts are the people used by the FOS to consider the complaint, I'm told they give the particular complaint to experts in that particular field, in my case mortgage interest.

Hi Thrugelmir,

Virgin Money use a month of 30.14 days I think they said, it is 365 divided by 12 to give twelve equal months.

The details are all in my original statement:
I lend you £100 at 12%.
At the end of the year you owe me £112.
If I charge you 1/12 of 12% per month, i.e. I take the simple interest rate and then apply it compound, then you will find you have paid me around 12.68%.

£100 + (12%x£100)= £112
i.e. 12% per year

but £100 x (1.01)^12= £112.68
i.e. add 1% each month to give an annual compound interest rate of 12.68%

ValHaller

People here do not seem to have engaged with this:

engineertony wrote: »

After I asked they have confirmed in a letter that the monthly rate being used is 5.49/12 i.e. 0.4575% per month.

So now I've been back to them to ask why they use the simple interest rate and then apply it at a compound rate on my balance. If I work out 5.49/12 compound I get 5.64%.

Either he has been wrongly advised about how the monthly payment is calculated or if they have advised the monthly rate correctly they are overcharging him in relation to the annual rate he has been quoted.

Thrugelmir

engineertony wrote: »

Virgin Money use a month of 30.14 days I think they said, it is 365 divided by 12 to give twelve equal months.

The actual systems themselves are programmed to calculate on an actual days basis.

engineertony

Hi everyone,

Hi Valhaller,

"People here do not seem to have engaged with this:"

I was surprised as this is supposed to be a money site with discussion on such topics. It's not that complex, indeed it's pretty basic schoolboy maths. The difference between simple and compound interest.

Imma_Number

Assuming: £100,000 Interest Only mortgage at 5.49%
If you were to pay all the 5.49% in one go (ie 1 rest) that would be £5490

Paying monthly over 12 months (12 rests):
£100,000 * (5.49%/12) = £457.50
£457.50 * 12 months = £5490

If you don't miss making the monthly payment it doesn't get compounded and so it's simple interest and you end up paying the same.

Why is having more rests better:
With 1 rest/year the interest is added at the beginning of the year. Any capital payments you make won't take effect until the next year.
With 12 rests/year the capital payment starts taking effect the next month.
eg Make capital payment in month 1 of £1000
1 rest: Interest charged £5490
12 rests: 1 month @ 457.50 + 11 months @ 411.75 = £4986.75
In both cases the balance at the start of year 2 is £90,000 but with scenario 2 you've saved £503.25 in interest.

#

Dave_the_Ginger_Cat

Just out of curiosity, what are you hoping to achieve from this?

engineertony

@Imma Number,

Virgin Money credit the borrower for payments at a rate of 5.49%/365 i.e. a daily rate of 1/365 th of the yearly rate.

The example you give is flawed because it takes no account of payments. If I don't pay or do pay monthly and whatever amount I pay makes no difference to my argument.
Each month they add 1/12 of 5.49% of the capital to my account, then the next month they add 1/12 of 5.49% to the account, and so on. Whether I pay some off or not is irrelevant, they are charging at a rate which is 5.63% per annum, as it is 1/12 of 5.49% compounded over 12 months.
By paying the interest monthly I keep the capital fixed and sure it looks like I've paid 12 x the monthly rate of 1/12 of 5.49% i.e. 5.49%.

From the other side consider you invest £100,000 in an account paying you 12% per annum and you demand 1/12th of 12% per month, that is 1% of £100,000. You will receive £1000 per month.
At the end of 12 months you have £12,000 and you have your 12%. But the bank has lost because you could have reinvested your £1000 each month, giving you a total of
£100,000 X (1.01)^12=£112,682.5
The bank has paid 12.68% not 12% as it first appears.

It is quite subtle and meant to fool the borrower, but it's wrong, they are effectively charging more than the nominal rate without informing the borrower.

@Dave the Ginger Cat,

If I win, then it looks like I'm owed around £5000 not counting the rate of inflation which was included with PPI payouts. If I lose I've lost nothing but I'll continue on sites like this until someone grasps the fiddle.
If that happens then it will be bigger than the PPI scandal, as all building society borrowers realise what is happening.

Imma_Number

engineertony wrote: »

@Imma Number,

Virgin Money credit the borrower for payments at a rate of 5.49%/365 i.e. a daily rate of 1/365 th of the yearly rate.

Ok that sounds much like the Nationwide (It's still 1/365th in a leap year. NW doesn't charge interest on Feb29th)

In my experience what they (NW at least) do is calculate 1/365th of the interest rate and add that same amount daily.

So going back to the earlier example: 100,000 @5.49%
Daily interest 5.49%/365 = 0.0001504109589
or £15.04109589 per day.
So
Day 1 accrues £15.041... interest
100000 + 15.04109589 = 100015.04109589
Day 2 accrues an additional £15.041... interest
100015.04109589 + 15.04109589 = 100030.082191781
...
Day 365 accrues an additional £15.041... interest.
105474.958904109 + 15.04109589 = 105490.0000000

If I am reading what you are writing correctly, you think they do this:
Day 1: 100,000 * (1+0.0001504109589) = 100,015.04109589

Day 2:
100,015.04109589 * (1+0.0001504109589) = 100030.084454126
...

Day 365:
105627.17291073 * (1+0.0001504109589) = 105643.060455455

My experience with this is from matching the interest NW charged me daily (yes, I logged in daily for > 5 years) with calculations.

My first attempt was to compound the interest daily but it would be very wrong by the end of the month. Switching to the simple interest method outlined above the calculations matched.

When the balance changes due to a payment of capital (and 01 Jan each year in NW's case) a new daily rate is calculated.

JakeWible

Yeah even I looking forward to know ,what are you hoping to achieve from this?So many calculation they are just not my cup of coffee.I usually use calculators for such calculations as general maths is not so strong.