How is APR calculated

MarkyMarkD

I will say this just once more then I will let it pass.
You do not actually pay the APR rate.
You pay the rate stated.

APR

That is an American website. Under UK APR regulations almost all costs are included within the APR and therefore it is the only basis for comparison for personal loans where you intend to keep them for the term.

As I've said on other threads, APRs are useless for mortgages because no MSE is going to keep the same mortgage for 25 years.

Almost all personal loan providers only quote an APR, not a confusing "flat" or "headline" rate. So, the payments ARE determined using the APR.

You may say "you pay the rate stated" but as it's a repayment loan, the payments are NOT as simple as "amount borrowed x rate stated".

Robert_Sterling_3

You can lead a horse to the water but you can't make him drink

You are not alone See paragraph a)

I have now removed the third link

MarkyMarkD

The first two links say more things about APR, from different angles, but don't contradict what I've said.

The third link is a duff link as it's a "modify" link (presumably to one of your own posts RS?)

Robert_Sterling_3

Have you still not grasped the fact that there is the rate of interest charged by the lender and there is an APR which is not the rate charged by the lender but is a number calculated from a number of ingredients one of which is the interest rate charged by the lender together with any charges associated with the loan. e. g. An arrangement fee etc.

To calculate the APR you have to subtract all the charges from the amount of the loan and then add them to the Total Cost of Credit.

MarkyMarkD

OK, let me summarise what I am saying (although it is becoming rather pointless to do so).

Mortgages

For mortgages, there is normally a quoted headline rate (e.g. 4.5%) and an APR (e.g. 5.5% APR).

If you had an interest only mortgage, you could calculate your payments exactly using the headline rate: 4.5% on a £100k mortgage is £4,500 per year or £375 per month.

The APR is higher than the headline rate due to:

(a) the rate not remaining at the headline rate throughout the term (the main reason); and
(b) charges being exercised (a very minor part of the difference).

The APR is calculated as the internal rate of return of all of the cashflows throughout the loan's life (i.e. the rate at which the net present value of all the cashflows comes to zero).

But, if you have a repayment mortgage, you wouldn't be able to work out the payments directly from the headline rate, as you need to deal with the repayments of capital.

Personal loans

Personal loans used to operate as above, but normally lenders do not bother to quote a headline rate as it's just confusing to do so. Personal loans are never interest only, so nobody can calculate payments which mean anything using the advance x the headline rate.

Lenders work out the repayments on a personal loan by doing the APR calculation backwards - in other words, they work out the monthly payments which make the net present value of the discounted cashflows zero, at the quoted APR.


For personal loans, APR is everything. It's all that matters in comparing products. For mortgages, APR is irrelevant unless you are going to keep your loan for 25 years which would be a bad move for other reasons.


As regards the deduction of fees which are charged up front, you are correct that these form part of the total cost of credit and hence part of the APR.

Robert_Sterling_3

Mortgages
For mortgages, there is normally a quoted headline rate (e.g. 4.5%) and an APR (e.g. 5.5% APR).
If you had an interest only mortgage, you could calculate your payments exactly using the headline rate: 4.5% on a £100k mortgage is £4,500 per year or £375 per month.

If it is an interest only mortgage at 4.5% then the monthly payments would be about £367.48 per month unless you are using a now discredited system where you pay 1/12 th of the annual rate each month.
With your monthly payment the APR is higher than the 4.5% rate because you have divided by 12 to get the monthly rate which you make 0.00375% but you should have extracted the twelvth root of 1.045 to get 1.0034748 and then subtracted 1 to get the monthly rate 0.0034748%
Your APR should be 4.5% but you are using an APR of 4.5939825% of 4.594%.
This confirms my theory that you do not understand APRs.

Robert_Sterling_3

I was expecting an answer but answer came there none.

Freddie_Snowbits

Sorry, but I am totally lost on APR. My bank, IF have an APR of 11.9% on its Credits Cards, which is fine because of offsetting, I paid £11 last year on an average balance of £750, which is considerably less than 11.9%.

But what is AER, EAR? ;D ;D ;D

MarkyMarkD

I was expecting an answer   but answer came there none.

I've been busy.

As usual, you are wrong.

Read my post properly.

Headline rate 4.5%. Nothing to do with APRs. At a headline rate of 4.5%, the interest payable on an interest-only £100k mortgage is £4,500 which is £375 per month.

There's nothing "discredited" about calculating the monthly payment as 1/12 of the annual payment - that's the only way to do it, other than the pedantic method (presumably favoured by yourself) of dividing the annual payment by 365 (and, pedantically, 366 in a leap year) and then calculating each month's payment by multiplying it by 28,29,30 or 31 depending on the number of days in each month. But no institution does it that way.

I do understand APRs, but you do not appear to understand English.

MarkyMarkD

Sorry, but I am totally lost on APR. My bank, IF have an APR of 11.9% on its Credits Cards, which is fine because of offsetting, I paid £11 last year on an average balance of £750, which is considerably less than 11.9%.

But what is AER, EAR? ;D ;D ;D

AER is normally a savings term - it's the Annual Equivalent Rate. It means how much interest you will receive over the first year, in general.

EAR isn't a very commonly used term.