BM5.3 – The Present Value Formula

Chapter 5, Lesson 3

In this lesson students will:

• use a time diagram to develop the present value formula
• calculate the present value of an ordinary simple annuity

Present Value – Ordinary Simple Annuities

The Time Diagram Approach

Let’s begin this lesson by observing a time diagram of an ordinary simple annuity, similar to what we did in Lesson 5.2. Equivalent payments will be labelled as $PMT$, and payment frequencies we use $t_{n}$. The video below will guide you through the formulation of the present value formula for an ordinary simple annuity.

Present Value Formula Examples

As we saw in our previous video, the present value formula for an ordinary simple annuity is:

\begin{aligned} P &= PMT \left[ \frac{1-(1+i)^{-n}}{i} \right] \end{aligned}

Let’s work through a couple examples to help solidify our use of the formula.