Mathematics of Finance Formulas by mmcsx

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									                                                   Mathematics of Finance
                                                        Formulas

Simple Interest: i = prt

Amount with compound interest:                    A = P(1 + i ) n   or   FV = PV (1 + i ) n

Amount with continuous compound interest:                    A = Pert     or       FV = PV ⋅ e rt


Annuity – account into which a person makes equal periodic payments or receives equal periodic
payments.

Annuities certain – annuity in which payments begin and end on fixed dates.
  Two types of annuities certain that will be considered are ordinary annuity and annuities due.

Ordinary annuity – type of annuity certain in which payments are made at the end of each of equal
payments intervals.
        Future value (amount of annuity)          Present value (single sum of money required to
                                                  purchase an annuity that will provide payments at
                         (1 + i ) − 1 
                                  n               regular intervals)
           FV = PMT                                                               1 − (1 + i ) − n 
                                             i                           PV = PMT 
                                                                                           i          
                                                                                                     

Annuities due – type of annuity certain in which periodic payments are made at the beginning of the
period. Term is from the first payment to the end of one period after the last payment (which adds one
more payment and which is why one payment is subtracted).
                         (1 + i ) n +1 − 1 
               FV = PMT                     − PMT
                                 i         


Deferred Annuity – first payment is not made at beginning or end of first period but at some later time.
                  1 − (1 + i ) − ( n + k )   1 − (1 + i ) − k        1 − (1 + i ) − n           −k
         PV = PMT                          −                   = PMT                   (1 + i )
                          i                        i                       i          

        where n = # of periods; k = # of periods deferred; i = interest rate per period


Annuity, where interest is compounded continuously but payments of $P are made m times per year for
a term of T years.
               mP(e rT − 1)                                                     mP(1 − e − rT )
          FV =                                                             PV =
                   r                                                                 r


Future Value of an Income Stream after T yrs                             Present Value of an Income Stream of
of $ R (t ) per year, earning interest at rate of                        $ R(t ) per year, earning interest at rate of r per
r per year, compounded continuously is                                   year, compounded continuously is
                      T                                                                 T

                      ∫ R(t ) e                                                         ∫ R(t ) e
                                                                                                    − rt
        FV = e   rt               − rt
                                         dt                                    PV =                        dt
                      0                                                                 0

								
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