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TVM Formula

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					N
u
       Time Value of
m                                                                 Compounded (m) Times per                         Continuous
      Money Formula           Annual Compounding
b                                                                         Year                                    Compounding
            For:
e
r
                                                                                                   nm
     Future Value of a                                                               i 
1                                 F V = P V (1+ i )    n
                                                                          FV = PV 1 +                               FV = PV( e )in
     Lump Sum. ( FVIFi,n )
                                                                                   m
                                                                                                   - nm
     Present Value of a                                                                     i 
2                                 PV = FV ( 1 + i )-n                 PV = FV 1 +                               PV = FV( e )-in
     Lump Sum. ( PVIFi,n )
                                                                                       m
     Future Value of an                      ( 1 + i )n - 1                      1  (i / m) nm  1
3                            FVA = PMT                          FVA  PMT                                
     Annuity. ( FVIFAi,n )
                                                    i                                    i/m             
     Present Value of an                    1 - ( 1 + i ) 
                                                          -n
                                                                                 1 -  1 + (i / m)  - nm

4                            PVA = PMT                         PVA = PMT                                  
     Annuity. ( PVIFAi,n )
                                                   i                                     i /m             
     Present Value of a                         PMT                                       PMT
5                               PVperpetuity                       PV perpetuity 
     Perpetuity.                                   i                                 [(1  i )1/ m  1]
                                                                                               m
     Effective Annual                                                              i 
6
     Rate given the APR.             EAR = APR                           EAR =  1 +  - 1                            EAR = e i - 1
                                                                                   m

     The length of time                                                         ln ( FV/PV)
                                      ln (FV/PV)                         n=                                           1
7    required for a PV to          n=
                                                                              m * ln  1               
                                                                                           i                     n=     * ln ( FV/PV)
     grow to a FV.                     ln (1 + i )                                                                    i
                                                                                           m

     The APR required for
                                        FV 
                                                1/ n                            FV 1/( nm )                       1
8    a PV to grow to a               i=     -1                       i = m *             - 1               i=     * ln (FV/PV)
     FV.                                PV                                    PV 
                                                                                                
                                                                                                                     n


     The length of time                                                     i  FVA m 
     required for a series             (FVA)( i )                     ln         + 
                                   ln               + 1                   m  PMT i 
9    of PMT’s to grow to               PMT                         n=
     a future amount
                                n=                                                   i 
                                         ln (1 + i )                       m * ln 1 + 
     (FVA).                                                                       m 

                                                                            (PVA )(i / m) 
                                      (PVA )(i )                      ln 1             
     The length of time           ln 1                             n                  ,
                                                                                  PMT
     required for a series                   PMT 
10   of PMT’s to exhaust       n                 ,                              i 
                                                                          m * ln 1  
                                        ln (1  i )
     a specific present                                                           m 
     amount (PVA).
                                    for PVA(i) < PMT
                                                                           for PVA(i/m) < PMT

                                                      Legend
       i = the nominal or Annual Percentage Rate                                   n = the number of periods
  m = the number of compounding periods per year                                EAR = the Effective Annual Rate
ln = the natural logarithm, the logarithm to the base e                 e = the base of the natural logarithm ≈ 2.71828
         PMT = the periodic payment or cash flow                                 Perpetuity = an infinite annuity


                                                                            Prepared by Jim Keys

				
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