# BM8.2 – Determining Equivalent Payments

Chapter 8, Lesson 2

In this lesson students will:

• calculate PMT given information about the future value or principle amount of an general annuity due

## Calculating the Equivalent Payment Size

In Lesson 6.3 we developed a method for solving for the equivalent payment size for an annuity due. Recall that the procedure to solve a problem involving a general annuity is to first calculate an equivalent interest rate $i_{2}$. Once we know this periodic rate, we can substitute it into our annuity due formulas. If we know the future value of the annuity we are working with then the formula below will apply. We will solve for PMT in the formula.

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

If we know the present value of the annuity we are working with them the formula below will apply. We will solve for PMT in the formula.

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

In the video below we will explore how to utilize the formulas listed above, as well as allow our TI BA II Plus calculator to evaluate the answers we require.