# BM8.1 – Finding Present and Future Value

Chapter 8, Lesson 1

In this lesson students will:

• calculate the future value of a general annuity due
• calculate the principle amount of a general annuity due

## Future Value – General Annuities Due

Recall from Lesson 7.1 the general annuity problem occurs when the compounding frequency is not equal to the payment frequency ($f_{1} \neq f_{2}$). In order to solve this problem throughout Chapter 7, we used an equivalent interest rate to ensure that $f_{1}=f_{2}$. As with other general annuities, our first step when working with a general annuity will be to calculate $i_{2} = \left( 1 + i_{1} \right)^{f_{1}/f_{2}}$. After this, we substitute the new periodic rate $i_{2}$ into our annuity due future value formula.

\begin{aligned} FV &= PMT \left[ \frac{(1+i_{2})^{n}-1}{i_{2}} \right] (1+i_{2}) \end{aligned}

Let’s look at an example of how we utilize this procedure. After we have used the formula, we will answer the question using the TMV buttons on our calculator as well.

## Present Value – General Annuities Due

Suppose now we are given information regarding the present value (principle amount). Similar to what we did above, we will first calculate the equivalent interest rate $i_{2}$, then substitute this new periodic rate into our formula for the present value.

\begin{aligned} P &= PMT \left[ \frac{1 - (1+i_{2})^{-n}}{i_{2}} \right](1+i_{2}) \end{aligned}

Let’s look at an example of how to use this procedure. After we have used the formula, we will answer the question using the TMV buttons on our calculator as well.