Converting interest per day into APR.

Daily interest payments can be calculated from the APR by simple division. This was pretty damn accurate for my mortgage.

The equivalent daily interest rate (daily compounded) requires that you take the 364th root. If I am wrong I am sure someone will be along shortly...

I believe the secret clue is in the "A" in APR, i.e. it is annualised.

No.

If it is an interest only mortgage with annual rests then you are correct. But you cant apply the same principle universally.

Who compounds daily?

Ronald will be along soon.

Actually, it only 'annual'.

Anyway the OP asked the question the other way round, i.e. derive the APR from a daily rate. For this to be done then we need to know the period for which the interest accrues before it is added to the principal. Some lenders do it monthly, others annually and a few quarterly.

Mine was interest only, but offset. I would only ever have a mortgage that charged daily interest. There are 2nd order effects as the monthly payments are fixed based on the original loan amount (ignore any offset). So each month the 'interest only' payments actually include more than just interest and it is not clear when/how this excess payment impacts the interest payable.

AFAIK that was what the OP was asking.

Waiting with anticipaton...

Then you must have been using the contract rate, not the APR.

Why 364? Do we get Valentine's Day off?

Never work from the APR, it's a useless legalese figure which takes into account things other than interest. Therefore it is in general impossible to compute the real rate actually charged from a given APR.

Work from the contract (or nominal) annual rate. Divide it by the number of periods in the year at the end of which accrued interest is added to the account. Then you can calculate your own TAR (true annual rate) by raising the periodic interest factor to the power of the number of periods in the year.

It is extremely unlikely that you would find an account which adds (and hence compounds) interest daily. But if you did find one, and if the contract annual rate were [conveniently] 3.65%, this would correspond to a daily rate of 0.01%. To compute your own TAR, you would raise 1.0001 to the power 365 to get 1.03717, so the TAR would be 3.717%.

Hypothetically, if you had been given a TAR of 3.717% and told it compounds daily, then you could calculate the daily rate by taking the 365th root of 1.03717 (or raising it to the power 1/365) to get back to 1.0001 => 0.01%.

In message , snipped-for-privacy@yahoo.co.uk writes

It will reduce the capital upon which the daily accrual is calculated.

Not as far as I can see. Daily compounding is extremely rare indeed, in fact I dontknow a mainstream mortgage lender who does that.

Same here.... (whistles impatiently..........)

The annualised daily compounding rate is almost identical to the annualised continuously compounding rate.

Most financial mathematicians use the continuously compounding rate as the formulas produced (using logs and the exponential function) are easier to handle.

You have to be a bit careful with your language. Annual compound rates are used for periods less than a year and they are still compound rates.

A compound interest rate can be quoted as Annual, Semi-Annual, Daily or Continuous, provided these rates are equivalent they will calculate the same interest for the same period. Its a bit like measuring in Kilo's or Pounds.

Simple rates are different.

APR takes into account any fees or incentives. In addition if there is a tiered interest rate (such as a discount period) then this is also used. For the latter case assumptions must be made about the length of the mortgage since few go to full term, I believe.

I remember the days of MIRAS: APRs were fiendishly difficult to calculate then ;-)

Mark

Agree, APR is a fudge which is meant to allow people to compare accounts.

I have no idea what contract rate; I only use the value on my mortgage statement.

Daily compond interest is practically unheard of but daily interest charging is very common (and highly desirable) for any offset mortgage. This daily interest works by simple division by # of days (or at lesat mine does).

And fails miserably at that because it assumes too much, and above all else it assumes you will stay with the lender for the whole term. Even when it was very rare for borrowers to switch lenders without moving, this was daft because the average person/couple/family did not buy just one house to last them into the grave, but sold up and re-bought after typically 7 years, so working to a 25-year loan plan was not terribly helpful. In particular, amortising fees over 25 years if the loan is going to be cut short is unrealistic.

That'll be it. In advertising, the APR has to be given maximum prominence over (or joint maximum prominence with) the nominal contract rate, but on your statements I'm not sure that's the case.

Indeed, it would be utter madness not to accrue daily in such circumstances. Only in pure mortgage accounts, where there is only one transaction a month is it at all reasonable to accrue monthly. Some scoundrel lenders even accrued yearly (don't know if many still do), which meant they charged you a whole year's interest on the whole loan balance as it stood at the beginning of the year *even though* you were reducing the balance with your monthly payments.

In message , Nick writes

What do you mean by that? The interest is applied daily?

It is the convention to quote interest rates in an annual form regardless of the compounding frequency.

Hence interest over a number of days from an annualised daily compounding rate r is calculated as

interest = 100 * ((( 1 + (r / 365) /100) ^ days ) -1)

This means Annual, Semi Annual, Daily and Continuous compounding rates are ballpark similar.

For instance the following rates are equivalent

Its all basically exponential growth.

Thanks for the responses. Just to clarify: I was referring to a credit card account. I have a low inteest rate on that account, and pay the minimum payment each month. (The rate is better than any bank loan I've been offered.)

But I now have a new question on the same subject: I want to charge interest on overdue incoming rent, equating to about

A W

If you want to express the rate as an annual rate, and if this is to be 30%pa, then you are better off with a simple rate not compounding daily (unless you expect rent (or outstanding interest) to be more than a year overdue.

The simple daily rate which corresponds to 30%pa is 0.08219%pd, but the compound daily rate which corresponds to 30%pa is only 0.07191%pd.

So if £500 rent is 6 weeks late (42 days), the interest using compounding would be (1.0007191^42-1)*£500 = £15.33 but using simple interest it would be 0.0008219*42*£500 = £17.26.

Bringing in fancy arithmetic to deal with compounding at any frequency is not particularly helpful and it's best to keep things simple, especially if you want to stand a chance of enforcing it in court should it come to that.

If your tenants are persistently late with the rent, rather than charging interest it might be better in the long run to replace them.

Very good point. Thanks!

A W

Not with my bank account :-(

In message , A W writes

Dont use a 'compound' rate. Use a simple rate.

Charge a rate linked to your own bank's base rate, i.e 5% over HSBC base rate. 30% is too high..

Is it? Well, OK, perhaps it is, so long as he adds a £30 admin charge as well.