1.4 Annuities

Annuity

An annuity is a financial instrument or series of cash flows that pays a fixed amount of money at $n$ intervals per year for $t$ years, with each payment $C$ remaining constant over the term. The payments can be made at the end of each period (ordinary annuity) or at the beginning (annuity due). Formally, the present value of an ordinary annuity, given an annual percentage rate $r$, is expressed as:
$PV=C\times \left[\frac{1}{r}-\frac{1}{r(1+r{)}^{nt}}\right].$

Additionally, a growth perpetuity is a perpetuity that grows at a constant rate of $g$ per year given a principal $C$:
$PV=C\times \frac{1}{r-g}\left[1-{\left(\frac{1+g}{1+r}\right)}^{nt}\right].$

No Initial Payment $t_0$. The formula for an annuity-due is given as:

Just like with perpetuities, standard annuities do not offer payment at