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Date: Sun, 17 Aug 2008 00:17:39 +0100
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To: Commons Users List <user@commons.apache.org>,
 david.hoffer@issinc.com
Subject: Re: commons-math usage to calculate APR?
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From: Rory Winston <rory.winston@gmail.com>

If your loan fees are expressed as a fixed amount you may be able to
represent the total PV of the loan as loan amount + fees, and then solve
for the monthly payment amount using the annuity formula:

PV = C(1/r - 1/(r(1+r)^t))
=> C = PV/(1/r  - 1/(r(1+r)^t))

Then you can build a payment schedule and calculate the APR of the
entire loan plus fees by calculating the IRR of the cash flows. Do you
actually need commons-math to do this? Could you do it in Excel instead,
using the IRR() or PMT() functions? That would probably be easier.

Rory

David Hoffer wrote:
> Luc,
>
> It's not clear to me that I could.  See another email I just sent for the
> approximate formula.
>
> I think Newton-Raphson or Bisection can be used to solve the non-linear part
> but I don't know how.
>
> -Dave
>
> -----Original Message-----
> From: Luc Maisonobe [mailto:Luc.Maisonobe@free.fr] 
> Sent: Saturday, August 16, 2008 3:45 PM
> To: Commons Users List
> Subject: Re: commons-math usage to calculate APR?
>
> David Hoffer a �crit :
>   
>> My usage is for USA only at this point.  
>>
>> I have inputs of loanAmount, monthlyInterestRate, numberMonths, loanFees;
>>     
> so
>   
>> this would be for fixed monthly payments.  
>>     
>
> You can try this (considering monthlyInterestRate is a number between
> 0.0 and 1.0, i.e. percent values have already been divided by 100.0, and
> considering the loanFees are fixed monthly fees):
>
>   public double getMonthlyPayment(final double loanAmount,
>                                   final double monthlyInterestRate,
>                                   final int numberMonths,
>                                   final double loanFees) {
>      final double f = Math.pow(1 + monthlyInterestRate, numberMonths);
>      return loanFees + monthlyInterestRate * f * loanAmount / (f - 1);
>   }
>
> Could you compute the APR from this monthly payment ?
>
> Luc
>
>   
>> I understand that commons-math doesn't have specific finance methods
>>     
> however
>   
>> I think the APR formula is a non-linear equation that I was hoping
>> commons-math could help solve.
>>
>> -Dave
>>
>> -----Original Message-----
>> From: Luc Maisonobe [mailto:Luc.Maisonobe@free.fr] 
>> Sent: Saturday, August 16, 2008 2:45 PM
>> To: Commons Users List
>> Subject: Re: commons-math usage to calculate APR?
>>
>> David Hoffer a �crit :
>>     
>>> Can anyone point me to an example of how to use commons-math to calculate
>>> APR (Annual Percentage Rate)?  
>>>       
>> There are no specific finance related algorithm in commons-math.
>>
>>     
>>> I think this is solvable using either the NewtonSolver or BisectionSolver
>>> but I am not sure how to accomplish this.  Perhaps a different way is
>>> better.  
>>>       
>> I think so, but it depends on what you really need. APR computation
>> seems to be slightly different depending on local regulations (for
>> example USA or EU). It also depends on the assumptions you do and the
>> input data. For example you can compute it one way for fixed monthly
>> payments and another way for varying monthly payments.
>>
>>     
>>> Any help would be greatly appreciated.
>>>       
>> Could you explain your needs more precisely ?
>>
>> Luc
>>
>>     
>>> Thanks.
>>>
>>>
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>
>
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