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.