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Calculating APR - effect of an upfront fee

Posted on 2013-12-30
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Last Modified: 2014-01-06
Hello
I'm looking at this online apr calculator and I'm a bit confused as to why adding an upfront fee to a loan increases the apr so much

http://www.financecalcs.co.uk/smartcalcs/LoanCalculatorquote.php

For example, if i add a fee of £250 to a 10k loan over at 5% interest over a year the apr changes from 9.5%, the apr changes to 14% give or take depending on whether the fee is upfront or spread. I dont understand why this is so much higher than if i simply borrowed 10250 (where the apr stays at 9.5%). I know that doing this approximation isn't quite the same as having an upfront fee because an upfront fee would affect the value of the first monthly payment whereas all the payments are the same in my quick workaround , but even so i wouldnt expect this. In fact i would expect an upfront fee which is paid off in the first month and hence accrues hardly any interest would have negligible affect on APR?

Thanks in advance for any light you can shed
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Question by:andieje
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Expert Comment

by:nickg5
ID: 39751487
In that calculator what number are you entering in the space for "flat rate of interest"
Are you entering 0
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Author Comment

by:andieje
ID: 39752444
5%
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Accepted Solution

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nickg5 earned 2000 total points
ID: 39752506
Leave the $10,000 as $10,000. Then change the "upfront" to "spread" and you see that the 14.4% goes to 14.8%.

The actual interest is $500 or 5% of $10,000.
That same $500 is the "total charge for credit"

If you add the 250 as an arrangement fee then you see the "total charge for credit" is $749.96 which is accurate.

Now, change the $10,000 to $10,250 and leave the arrangement fee zero.
Now the "total charge for credit" is $512.56 which is also correct.

Why? Because you are "financing" the extra $250 at 5%. 5% x 250 = $12.50.

It's more simple to not use such calculators.
The 14.5 or the 14.8 or the 9.5 does not change the numbers.

If the 250 is part of the loan you pay 5% on that 250.
If 250 is not part of the loan but an arrangement fee then the entire 250 is added to the $500 interest and is excluded from the A.P.R. which is calculated on the loan amount of $10,000 at 5%. That is why you only see 9.5%

By adding the 250 as part of the total cost of credit you are increasing the "total" extra from $500 to $750.

So, since you are increasing the 5% or $500 by 50% by adding another $250 here is where
the 9.5% must also go up by 50%.

What is 50% of 9.5? It's 4.75
4.75 + 9.5 = 14.25 and basically completes the math on how the 9.5% gets to 14.4 or thereabouts.
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Author Closing Comment

by:andieje
ID: 39760753
Brilliant explanation - thank you
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