# BM7.2 – Finding Present and Future Value Chapter 7, Lesson 2

In this lesson students will:

• calculate the future value of an ordinary general annuity
• calculate the principle amount of an ordinary general annuity

## Future Value – Ordinary General Annuities

#### The Equivalent Interest Approach

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, we can use an equivalent interest rate to ensure that $f_{1}=f_{2}$. 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 can then use our future value formula and substitute in the new periodic rate $i_{2}$. \begin{aligned} FV &= PMT \left[ \frac{(1+i_{2})^{n}-1}{i_{2}} \right] \end{aligned}

Let’s look at an example of how we utilize this procedure.

#### The TVM Buttons Approach

We saw how to program annuity question into the TI BAII Plus calculator is Lesson 6.5. The main advantage of understanding how to use the time value of money buttons on the calculator is that it will automatically calculate $i_{2}$ using the information provided. Let’s work through the example we did above in order to verify the validity of our solution.

## Present Value – Ordinary General Annuities

#### The Equivalent Interest Approach

Once again, we will use the method from Lesson 7.1 to first calculate the equivalent interest rate $i_{2} = \left( 1+i_{1} \right)^{f_{1}/f_{2}}$. Once we have calculated this new periodic rate, we can substitute it into our formula for the present value. \begin{aligned} P &= PMT \left[ \frac{1 - (1+i_{2})^{-n}}{i_{2}} \right] \end{aligned}

Let’s look at an example of how to use this procedure.

#### The TVM Buttons Approach

Using the procedure discussed in Lesson 6.5, let’s work through the previous example one more time to verify the validity of our solution.