# BM3.8 – Determining Equivalent Payments

Chapter 3, Lesson 8

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

Often when saving or making payments, we deposit the same amount of money every time. For example, we might deposit $\300$ every month into a registered retirement savings plan (RRSP) account. When the size of payment is consistent over a long period of time, we call these equivalent payments. The focus on this lesson is to determine the size of an equivalent payment given some information about a future or principle value.

#### 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 $3.5\%$ simple interest, 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 analyze a case in which we have some information regarding the principle amount, and see how this differs from our last example. Suppose that we have a principle amount of $\10,000$ in our account today and that money can earn $3.5\%$ simple interest. 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?