# BM4.9 – Determining Equivalent Payments

Chapter 4, Lesson 9

In this lesson students will:

• understand what is meant by an equivalent payment and give an example of where they might be used
• calculate an equivalent payment amount given information about the future value or principle amount of money

## Equivalent Payments

Recall from Lesson 3.8 that an equivalent payment refers to a payment that is a consistent size over a period of time. For example, making a monthly mortgage payment of $\1500$ over the course of five years would be considered an equivalent monthly payment. In Lesson 3.8 we worked through a few examples using simple interest. In this chapter of our course, we would like to revisit this concept, but alter the interest to be compound interest. While this does change the computations slightly, the overall structure of the problem will remain similar.

#### Equivalent Payments and Future Value

Suppose we would like to invest a certain amount of money every three months, beginning three months from now, for the next year so that our last investment is twelve months from today. Our investment goal is to save up $\10,000$ by the end of this twelve-month period. If money can earn $3.5\%$ compounded quarterly, how much are the equivalent payments every three months? Let’s explore this question in the following video.

#### Equivalent Payments and Principle Amount

Let’s compare the last example with the following one where we know some information about the principle amount instead. Suppose that we have a principle amount of $\10,000$ in our account today and that money can earn $3.5\%$ compounded quarterly. We would like to withdraw equivalent amounts every three months, beginning today, for the next year in such a way that after our fourth withdrawal our account balance will be $\0$. What should be the size of the equivalent payments?