Annuity and Perpetuity

 Annuity refers to a constant cash flow repeated for t periods.

Annuity with no growth

PV(Annuity) = A * 1/r  *  [1 - 1/(1 + r)T]

FV (Annuity) = (1 + r)T * PV(Annuity)

Annuity with growth rate g 

PV(Annuity) = A * [1/r-g [1 - (1+g/1+r)T]] (if r !=  g)

PV (Annuity) = A * T/1+r  ( if r = g)

Perpetuity is an annuity with infinite maturity

Perpetuity with no growth

PV(Perpetuity) = A/r

Perpetuity with growth rate g

PV(Perpetuity) = A/r-g (r>g)