Question about APR

[Otispunkmeyer]

So with a loan, you pay interest and that interest is usually called Annual Percentage Rate.

But how do you work out what your monthly payments are say for a £10k loan over 5 years.

Becuase I assume that for the 1st year, the amount of interest paid on top of paying back the loan is based on the 10k, but the second year it is based on whatever principle is outstanding and the third year again it is based on what ever is left. (This is Amortisation right?... paying increasingly less amounts of interest for the life of the loan)

So, without first knowing what the monthly payments are, how do you know how much of the loan has been paid back? Im sure its a simple step, I just cant see it... Is there anywhere where I can actually follow the maths through?

[seaninog]

Otispunkmeyer said:

So with a loan, you pay interest and that interest is usually called Annual Percentage Rate.

Let me stop you right there, fella. The interest rate on the loan is not the same as the APR. Your loan's interest rate could be at 10% but the APR will take the interest rate ADD ANY FEES and treat them as interest over the life of the loan and now recalculate the rate to give you the Annual Percentage Rate (APR). It's supposed to make loans comparable by including all feee charges but it is still quite confusing

Otispunkmeyer said:

But how do you work out what your monthly payments are say for a £10k loan over 5 years.

Use an online calculator like the one on the bottom right of this homepage http://www.choice-loans.co.uk/

Otispunkmeyer said:

Because I assume that for the 1st year, the amount of interest paid on top of paying back the loan is based on the 10k, but the second year it is based on whatever principle is outstanding and the third year again it is based on what ever is left. (This is Amortisation right?... paying increasingly less amounts of interest for the life of the loan)

Hmm... No, I don't think so. Loans are set up so you pay a fixed amount for the life of the loan (assuming it's at a fixed rate that is). Each payment is the same but as you rightly point out payments at the start are more interest than principle but this changes over time, even if the total payment amount does not.

Otispunkmeyer said:

So, without first knowing what the monthly payments are, how do you know how much of the loan has been paid back? Im sure its a simple step, I just cant see it... Is there anywhere where I can actually follow the maths through?

I'm not sure but I guess you should ask the loan provider..?

Hope this helps (and I hope I'm right in my interpretation of the issues; feel free to correct anyone).

[bigbubba]

APR is a ridiculous measure of interest.

It is much better to compare loans by using the Flat rate, as has been said this excludes fees but it is much easier to compare the actual repayment portion of loans by comparing flat rates.

You will have seen place like Wonga offering APR's that go into the 1000's. Initially they seem ridiculous but if the loan is over a week, ie. 1/52 of a year then the Annual Percentage Rate is going to be astronomical even though the true total repayment proportion may only be 20% of the original amount borrowed.

The big issue that you will have is that you ring up direct lenders and ask them what the flat rate is and they will quote you the APR as they are just telephonists.

HTH

[Dr Jekyll]

A ballpark figure for reasonably short periods is to say that on a £10K loan you will owe about £5K half way through the period. So work out 3 years (or whatever) interest on £5k. It's a slight underestimate but gives a rough idea.

[sidicks]

bigbubba said:

APR is a ridiculous measure of interest.

I'm sorry but you are completely wrong - while the flat rate is easily understood it is not an informed measure for deciding whether a loan is good value or not!

The APR is the effective rate of interest charged, which takes into account all the costs in a loan and the timing of cashflows.

From this perspective, flat rate is fairly meaningless!!

bigbubba said:

It is much better to compare loans by using the Flat rate, as has been said this excludes fees but it is much easier to compare the actual repayment portion of loans by comparing flat rates.

As the flat rate ignores the timing of cashflows it is unsuitable for comparing loans where the cashflow profiles may be different (e.g. repayment loan versus PCP-type structures).

As the flat rate ignores the timing of cashflows it is unsuitable for comparing loans against (for example) bank account or investments where interest is paid.

bigbubba said:

You will have seen place like Wonga offering APR's that go into the 1000's. Initially they seem ridiculous but if the loan is over a week, ie. 1/52 of a year then the Annual Percentage Rate is going to be astronomical even though the true total repayment proportion may only be 20% of the original amount borrowed.

The big issue that you will have is that you ring up direct lenders and ask them what the flat rate is and they will quote you the APR as they are just telephonists.

HTH

Like it or not, the APR represents the true cost of the loan - in the example above it will be 2500% or whatever) - because of the nature of the calculation it is not usually used to compare short-dated loans of this nature.


I'm afraid you probably haven't helped the OP in the slightest!

OP - when comparing car loans (or PCPs), the APR should be your first focus, the 'total cost for credit' should be your second focus.

For a typical repayment loan, the true rate (i.e. the APR) is approximately twice the flat rate (as mentioned above, for a £10k loan the 'average' balance is £5k).

edited to add
To calculate the monhtly repayment for a loan, you can do the following:

1) Take the loan amount an multiply by the flat rate and then by the number of years of the loan (this is the total interest paid)

2) Add the interest paid from 1) to the loan amount to get the total amount paid

3) Divide the total amount paid by the number of monthly payments to get the amount of each monthly premium.

OR

1) Take the APR (i) and work out the monthly effective rate i(12) = (1+i)^(1/12)-1

2) Monthly premium (paid in arrears) = Loan amount * i(12) / ((1 - (1+i(12))^(-n))
(where n = number of monthly payments)

3) You can use i(12) to work out the amount of the loan outstanding at any point in time:

Loan outstanding = monthly payment * i(12) / ((1 - (1+i(12))^(-(n-t)))
(where t = number of payments made to date)

Then the interest charged = i(12) * loan outstanding, and the capital repaid = total repayment - interest charged.


Sidicks

Edited by sidicks on Tuesday 19th July 21:58

[sidicks]

anonymous said:

[redacted]

Following the example above, based on 8% APR (effective rate)

i= 8%
i(12) = 0.6434%

Monthly payment = £291.39 over 4 years

Total amount paid = 48 * £291.39 = £13,986.49
Total interest paid =13,986.49 - £12,000 = £1,986.49
Flat rate = £1,986.49 / 4 / 12 = 4.14%

(so APR is approximately twice flat rate)

Now interest charged on first payment = 0.6434% * £12,000 = £77.21
Capital repayment = £291.39 - £77.21 = £214.18

After 1 year, loan outstanding = £9,336.95 (so capital repaid = £2,663.05)
After 2 year, loan outstanding = £6,460.86 (so capital repaid = £5,539.14)
After 3 year, loan outstanding = £3,354.68 (so capital repaid = £8,645.32)

Sidicks

Edited by sidicks on Tuesday 19th July 21:30

[sidicks]

anonymous said:

[redacted]

Just trying to help the OP!

Sidicks