# BM5.4 – Determining Equivalent Payments

Chapter 5, Lesson 4

In this lesson students will:

• calculate PMT given information about the future value of an ordinary simple annuity
• calculate PMT given information about the principle amount (present value) of an ordinary simple annuity

## Calculating the Equivalent Payment Size

#### Given the Future Value

Recall the future value formula for an ordinary simple annuity.

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

Suppose that we have a certain financial goal that we would like to save up for by making equivalent payments to a savings account. For example, perhaps we would like to save $\10,000$ for our child’s future education needs. What should be the size of the month-end payments if we have ten years to make these payments and the rate remains constant at $3\%$ compounded monthly? Let’s determine the size of the equivalent payment in the following video.

#### Given the Principle Amount (Present Value)

Recall the present value formula for an ordinary simple annuity.

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

Suppose that we have borrowed a certain sum of money and that we would like to pay off this amount by making equivalent payments to the institution that gave us the loan. For example, suppose we borrow $\450,000$ to purchase a small condo unit. We have agreed to make bi-weekly payments and the end of each payment period over the span of 25 years. If the rate remains constant at $3\%$ compounded bi-weekly, what should be the size of the equal-sized payments? Let’s work on this scenario in the following video.