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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

883.0. "Help solving LOG/EXP equation needed..." by DELNI::MHARRIS (Mark Jay Harris, Term Srvr Mktg Mgr) Mon Jun 06 1988 17:16

    OK guys-
    	It's been a number of years since my education has 'refreshed'
    my mind regarding equation solving. The following is throwing me
    because of the exponents (and my text books are still boxed from
    my last move).
    
    	I am trying to solve the equation for each of the variables
    separately. In other words, I want to yield 4 equations that
    can be solved given 3 of the variables. The LOG and EXP are
    making me crazy! Can anyone help out or refresh me on the
    LOG/EXP rules?
    
    Thanks,
    
    Mark
    
                                                 - Term
                           ( 1 - ( 1 + Int Rate )        )
Principle / Payment  =  [ --------------------------------- ]
                                      Int Rate
T.RTitleUserPersonal
Name		DateLines
883.1three out of fourZFC::DERAMOI am, therefore I'll think.Mon Jun 06 1988 22:5932
     Well, you will be able to solve it for Principle, Payment,
     or Term given the other three; but not for Int Rate.
     That is usually calculated iteratively -- keep closing
     in on the interest rate until you get the value that
     fits in the equation.
     
     Solving for Principle or Payment in the equation is
     straightforward.  To solve for Term, you proceed like
     this:
     
              Prin * Intrate                    - Term
              -------------- = 1 - (1 + IntRate)
                 Payment                              
     
     so
                           - Term        Prin * IntRate
              (1 + IntRate)        = 1 - --------------
                                            Payment
     
     so
                                                  Prin * IntRate
              (- Term) LOG(1 + IntRate) = LOG(1 - --------------)
                                                     Payment     
     
     and finally,
                                    Prin * IntRate
                            LOG(1 - --------------)
                                       Payment
              Term = - -----------------------------------
                            LOG(1 + IntRate)
     
     Dan
883.23-1/2 out of the way...DELNI::MHARRISMark Jay Harris, Term Srvr Mktg MgrTue Jun 07 1988 03:418
    Thanks. I knew the LOG rules would *seem* familiar! I think I
    came up with the iterative process for the interest rate as well
    so I guess I am well on my way.
    
    Thanks again.
    
    Mark
883.3more LOG and EXP rules.ZFC::DERAMOI am, therefore I'll think.Tue Jun 07 1988 13:2523
     The only LOG rule I recall using in .1 was
     
                     Y
                LOG(X ) = Y LOG(X)
     
     If you are interested in other LOG and EXP rules, here
     are more:
     
                LOG(XY) = LOG(X) + LOG(Y)
     
                EXP( LOG(X) ) = X
     
                LOG( EXP(X) ) = X
     
                EXP( X + Y ) = EXP(X) EXP(Y)

                                    Y
                EXP(XY) = ( EXP(X) ) 
     
     Taking LOG or EXP of both sides of one of these usually
     gives another one on the list.
     
     Dan
883.4numbers , which larger?STAR::ABBASIi^(-i) = SQRT(exp(PI))Sun Jul 26 1992 06:309
    which is larger?
    
              1,000,000                     999,999
     1,000,000                or    1,000,001
    
    hint: no calculator needed ;-)
    
    /Nasser
883.5AUSSIE::GARSONTue Jul 28 1992 22:5647