How is daily interest calculated?

Robert_Sterling_3

Guess what?

A lender has three ways in which you could view Capital and Interest.

Suppose someone borrowed £3,600 and were paying back £5400 over six years. £75 per month for 72 months


Method One:

Horizontal Line on Graph Method

Each month you pay £50 off the capital £25 off the Interest.

Method Two

The Actuarial Method

They did it my way as explained in this thread.

Method Three

The Rule of 78 way.

Each month they looked at the settlement figure in accordance with the Consumer Credt Act at that time.

If there was no breach of contract and the loan was paid off correctly then it did not matter which way they looked at it.

One method was used for tax purposes.
One method was used for actuarial purposes.
One method was used for predictve purposes.

Those of you who think that charging 1/365 th of the Annual Rate to get the daily rate are looking at it in your own way.

If the loan is paid according to plan then you will get the right answer at the end of each year. If you are allowed to cease the loan halfway through the year without penalty then you will find that you "Do not get half the annual interest" Your method of calculation gives you too much interest in the first half of the year and too little in the second half of the year. The interest you get halfway through the year is found using the actuarial formula.


Is anybody still with me ..... ?

Robert_Sterling_3

Stompa wrote: »

On the assumption that the interest is calculated daily and compounded annually, then yes. The OP didn't explicitly state how often interest was paid (i.e. compounded), but given that the gross and AER rates were the same it presumably must be annually.

The fact that you get the right answer on the 365th day of the year does not mean that you got it right on any of the other 364 days of the year.

Stompa

Robert_Sterling wrote: »

The fact that you get the right answer on the 365th day of the year does not mean that you got it right on any of the other 364 days of the year.

You can draw an infinite number of curves that pass through two points!

Robert_Sterling_3

Exactly so.

Since someone might take all their money out of an instant access penalty free account on any day of the year the lender has to have an accurate method of working out the interest earned for any day in the year. Only the actuarial method does this.

rb10

Robert_Sterling wrote: »

Since someone might take all their money out of an instant access penalty free account on any day of the year the lender has to have an accurate method of working out the interest earned for any day in the year. Only the actuarial method does this.

But my way can do that as well. If it's £10,000, at 5%, and it's in there for 180 days, then you can use my way to work out that the interest paid would be 10,000 * 0.05 / 365 * 180 = £246.5753425.

How do you know that your method is the way that banks calculate it?

oldfella

How do you know that your method is the way that banks calculate it?

---

I use your method to check bank interest payments - its usually close but actual payments tend to vary a little each side of my calculation - I have always suspected they use a different method

Stompa

oldfella wrote: »

I use your method to check bank interest payments - its usually close but actual payments tend to vary a little each side of my calculation - I have always suspected they use a different method

Indeed, I've never found either method exactly matches the interest payment I receive.

rb10

They don't just guess interest payments! Someone must surely know what formula is used for the calculation!

sloughflint

Robert_Sterling wrote: »

For the cognescenti this is what you should do

Let R be the daily Rate

Let r be the annual rate

Then R= [ 1+r ]^( +1/+365) -1

In the example above

R = [ 1+0.05 ]^(+1/+365) -1 Which is 0.0133681%

Thus we do not divide the annual interest rate by 365

we extract a 365th root

I will bore you no more with the sum.

This method is only valid if the accounts compound interest on a daily basis. I do not know of many that do.(Egg is one I recently found out)

sloughflint

Robert_Sterling wrote: »

It is better to get 3% half yearly than 6% per annum.

I'm not sure quite what the issue is in this thread.

3% every six months will always be better than 6% yearly.
This is because 1.03^2= 1.0609 >1.06

Robert_Sterling wrote: »

Since someone might take all their money out of an instant access penalty free account on any day of the year the lender has to have an accurate method of working out the interest earned for any day in the year. Only the actuarial method does this.

Not true.

If interest is calculated daily but non compounded----> apply 1/365th of the gpa rate.

If interest is compounded daily

---

> use 365th root.

rb10 wrote: »

How do you know that your method is the way that banks calculate it?

The T&C should state if interest is compounded daily or not.