Level Payment Annuity

Study guide: Exam FM-2

A level payment annuity makes equal (level) payments at regular intervals — for a fixed term, or forever in a level perpetuity. It is the most basic annuity structure, forming the basis for Annuity Immediate, Annuity Due and loan amortization.

• For a level payment P, n-period annuity-immediate at rate i:

\text{PV} = P \cdot a_{\overline{n}|i}

= P \cdot \frac{1-v^n}{i}

\text{FV} = P \cdot s_{\overline{n}|i}

= P \cdot \frac{(1+i)^n - 1}{i}

• The symbols a_{\overline{n}|} (present value annuity factor) and s_{\overline{n}|} (accumulated value annuity factor) are standard actuarial notation.

Loan Repayment A $20,000 loan at 5\% effective annual interest is repaid with 5 level annual payments (end of year). Find the payment amount.

Answer

\begin{align*}
20{,}000 &= P \cdot a_{\overline{5}|5\%} \\
&= P \cdot \frac{1-(1.05)^{-5}}{0.05} \\
&= P \times 4.329477 \\
P &= \frac{20{,}000}{4.329477} \\
&= 4{,}619.50
\end{align*}