Finance

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					                                 Formulas for Finance Math

m = the number of compunding periods per year.
(annually m=1, semiannually m=2, quarterly m=4, monthly m=12, daily m=360)
r = the annual interest rate as a decimal. (12% = 0.12)
t = the time in years. (6 months = 0.5 years)



                                          Simple Interest
                                           (P = principal)

Simple Interest                           Future Value                        Present Value
                                                                                      A
  I = Prt                                 A = P + Prt                         P=
                                                                                   (1 + rt )


                                        Compound Interest
                                          (P = principal)

  Future Value                              Present Value                     Continuous Compounding
                                                                                   ( e = 2.71828)
                  m⋅t
         r                                        A
A = P 1 +                               P=                                  A = Per⋅t        P = Ae−r⋅t
      m                                         r
                                                         m⋅t

                                               1 + 
                                                m



                           Future Value: Annuities and Sinking Funds
                               (FV = future value, PMT = payment)


                        r
                             m⋅t
                                                                             r     
                    1 +  − 1                                                    
                     m                                                        m
         FV = PMT                                            PMT = FV               
                         r                                                r
                                                                                   m⋅t
                                                                                       
                                                                      1 +  − 1
                         m                                            m         



                            Present Value: Annuities and Amortization
                                (PV = present value, PMT = payment)


                           r
                                − m⋅t
                                                                              r         
                  1 −  1 +                                                           
         PV = PMT   m                                      PMT = PV         m        
                          r                                                  r
                                                                                      − m⋅t
                                                                                            
                                                                    1 −  1 +         
                          m                                           m              

				
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