BM6.2 – The Present Value Formula

Chapter 6, Lesson 2

In this lesson students will:

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

Present Value – Simple Annuities Due

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 6.1. 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 a simple annuity due.

Present Value Formula Examples

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

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

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