Dyalog Programming Contest 2010 - Formulae

The bank loan is amortized though equal payments over the entire term, using the following formulas:

    BANKMR = Bank monthly mortgage rate
               = BANKRATE/12

    BANKPMT = Bank monthly payment
               = BANKAMT x BANKMR/(1-(1+BANKMR)^-TERM)

    BANKBAL[0] = Initial bank loan balance
               = BANKAMT

    BANKINT[I] = Bank mortgage interest in month I
               = BANKBAL[I-1] x MORATE

    BANKPRN[I] = Bank principal repaid in month I
               = BANKPMT - BANKINT[I]

    BANKBAL[I] = Bank loan balance after month I
               = BANKBAL[I-1] - BANKPRN[I]

Formulae for the following five items are parallel to the above formulas:

        DADMR = Parent monthly mortgage rate
        DADPMT = Parent monthly payment
        DADBAL = Parent loan balance
        DADINT = Parent mortgage interest
        DADPRN = Parent principal repaid

The remaining values are computed as follows:

    HOMEVAL[0] = Initial value of home

    HOMEVAL[I] = Value of home after month I
               = HOMEVAL[I-1] x ((1+INFL)^(1/12))
           (Home value appreciates at inflation rate)

    PROPTAX[I] = Property taxes paid during month I
               = HOMEVAL[I-6] x PROPRATE/2
                 (for months 6, 18, 30, 42,...)
               = HOMEVAL[I-12] x PROPRATE/2
                 (for months 12, 24, 36, 48,...)
           (Property taxes are computed annually and
            paid semiannually)

    TAXSAVE[I] = Mortgage tax savings during month I
               = BANKINT[I] x TAXRATE
           (Interest portion of bank mortgage payments are
            tax-deductible; payments to parents are not)

    SAVEOWN[0] = Initial savings while owning
               = 0

    SAVEOWN[I] = Savings while owning, through month I
               = (SAVEOWN[I-1] x (SAVRATE/12) x (1-TAXRATE))+
                 TAXSAVE[I] - (PROPTAX[I] + BANKPMT + DADPMT)

    HOMECASH[I] = Home cashout value, after month I
               = HOMEVAL[I] + SAVEOWN[I] -
                 (BANKBAL[I] + DADBAL[I])

     MORENT[0] = Initial monthly rent payment
               = INITRENT

     MORENT[I] = Monthly rent payment
               = MORENT[I-1] x (1+INFL)
                 (for months 13, 25, 37, 49,...)
               = MORENT[I-1]
                 (for all other months)
           (Rent increases once a year, at inflation rate)

    SAVERENT[0] = Initial savings while renting
               = (PRICE + COSTS) - (BANKAMT + DADAMT)
           (This amount is saved by not buying)

    SAVERENT[I] = Savings while renting, through month I
               = (SAVERENT[I-1] x (SAVRATE/12) x (1-TAXRATE))
                 - MORENT

    ADVAN[I] = Advantage (disadvantage) of buying
               = HOMECASH[I] - SAVERENT[I]