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Math Help - Loan formula

  1. #1
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    Loan formula

    Hi,

    I am very new to financial mathematics and I am looking for a loan formula to calculate a loan.
    I am writing a script (in Perl) to calculate leasing offers out of a price where you got a 10% scrap value (after the end of the contract you can buy the car for 10% of its original value).

    The problem is that the formulas (that i can find at least) do not have the FV (future value ) included in it and this is part of my needs. I found a perl module Math::Financial but this does not support the FV parameter in the loan calculation. In Open/Libre Office there is an existent function called PMT that does the trick but I need the actual formula behind that.
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  2. #2
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    Re: Loan formula

    The PMT function calculates the periodic payment to pay off the loan in full.
    Formula is:
    P = Ai / (1 - v) where v = 1/(1 + i)^n

    P = periodic payment
    A = Amount borrowed
    i = periodic interest rate
    n = number of periods

    In most cases, the payment frequency is monthly.

    As example, $15,000 is borrowed; 12% annual compounded monthly; 36 months:
    P = 15000(.01) / [1 - 1/(1.01)^36] = 498.2146.....
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  3. #3
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    Re: Loan formula

    Apparently I did not explained it correctly ...

    I got :

    rate (IR) - duration (N) - initial amount (PV) - scrap value (FV)

    I need payment (PMT)
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  4. #4
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    Re: Loan formula

    Quote Originally Posted by elfranne View Post
    Apparently I did not explained it correctly ...
    I got :
    rate (IR) - duration (N) - initial amount (PV) - scrap value (FV)
    I need payment (PMT)
    The formula I gave you is for regular loans...

    You stated:
    "In Open/Libre Office there is an existent function called PMT
    that does the trick but I need the actual formula behind that."
    Please supply an example of input and output.

    Apart from that, your problem as stated is unclear; like,
    is a "loan" really involved? Is the FV a balance owing on
    this loan, or is the loan first reduced to zero, then car sold?

    I suggest you google your topic; you'll get sites like:
    Lease vs Buy Calculator - Compare Car Leasing and Buying Costs
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  5. #5
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    Re: Loan formula

    BUT...if the objective is to calculate the payment (lease) on a loan where a known
    amount (scrap value) remains owing after nth payment, then formula is:

    P = i[A(1 + i)^n - S] / [(1 + i)^n - 1]

    P = periodic payment
    A = Amount borrowed
    S = Scrap value (known as balloon payment)
    i = periodic interest rate
    n = number of periods

    A simple example: loan of 5000, 12%, 36 months, scrap value 1000; comparing:
    Code:
        PAYMENT  INTEREST   BALANCE    PAYMENT  INTEREST   BALANCE
    00                      5000.00                        5000.00
    01 -166.07    50.00     4883.93    -142.85   50.00     4907.15
    ...
    36 -166.07     1.64         .00    -142.85   11.32     1000.00
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  6. #6
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    Re: Loan formula

    Quote Originally Posted by elfranne View Post
    Apparently I did not explained it correctly ...

    I got :

    rate (IR) - duration (N) - initial amount (PV) - scrap value (FV)

    I need payment (PMT)
    Most spreadsheet programs like MS Excel make use of an equation to find the five TVM or time value of money functions

    PV (1+IR)^N + PMT(1+IR * TYPE) [{(1+IR)^N} - 1]/IR + FV = 0

    TYPE is 0 for end of payments as in ordinary annuity e.g. mortgage payments
    TYPE is 1 for start of payments as in annuity due e.g. rent payments, lease payments

    So the PMT is singled out on the left hand side of the equation

    PMT = (-FV - PV * fvif(IR,N)) / (fvifa(IR,N) * (1.0+TYPE*IR))

    fvif(IR,N) = (1+IR)^N
    fvifa(IR,N) = [{(1+IR)^N} - 1 ]/IR

    You can try this PMT calculator to see if you get the correct payment before you implement this formula in Perl
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  7. #7
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    Re: Loan formula

    Quote Originally Posted by Wilmer View Post
    P = i[A(1 + i)^n - S] / [(1 + i)^n - 1]
    That was exactly what i was looking for. Sorry for being unclear about the info I gave you, because I am myself quite unclear on how it has to be because i have nearly never done any financial math ...

    Going to try to use it on my perl script now ...

    Thanks a lot
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