# BM6.1 – The Future Value Formula

Chapter 6, Lesson 1

In this lesson students will:

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

## Future Value – Simple Annuities Due

#### The Time Diagram Approach

In this lesson, our focus will be to develop and use the future value formula for simple annuities due. Recall that an annuity due is a payment stream where the equal-sized payments $PMT$ occur at the beginning of the payment period; and that a simple annuity has the property that payment and compound frequencies are equal ($f_{1}=f_{2}$). Due to this subtle change, the formula we have been using for ordinary simple annuities will not apply. We can, however, alter it slightly to make it usable for simple annuities due. The video below will show you how we make this small alteration.

#### Future Value Formula Examples

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

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

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