Level Annuity

Study guide: Exam FM-2

A level annuity is an annuity with equal, constant payments at regular intervals. It is synonymous with Level Payment Annuity and is the standard annuity type. The two main forms are:

• Annuity Immediate: payments at the end of each period; PV factor a_{\overline{n}|} = (1-v^n)/i

• Annuity Due: payments at the beginning of each period; PV factor \ddot{a}_{\overline{n}|} = (1-v^n)/d

• The relationship between the two: \ddot{a}_{\overline{n}|} = (1+i) \cdot a_{\overline{n}|}.

• Level annuities are used to model loan repayments, regular deposits, and structured insurance payments.

Annuity-Immediate vs. Annuity-Due Find the PV of a 4-year level annuity paying 1{,}000/year at i=5\%, both immediate and due.

Answer

\begin{align*}
\text{Immediate: } 1{,}000\,a_{\overline{4}|5\%} &= 1{,}000 \times 3.545951 \\
&= 3{,}545.95 \\
\text{Due: } 1{,}000\,\ddot{a}_{\overline{4}|5\%} &= 1.05 \times 3{,}545.951 \\
&= 3{,}723.25
\end{align*}