# BM6.3 – Determining Equivalent Payments

Chapter 6, Lesson 3

In this lesson students will:

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

## Calculating the Equivalent Payment Size

#### Given the Future Value

Recall the future value formula for a simple annuity due.

\begin{aligned} FV &= PMT \left[ \frac{(1+i)^{n}-1}{i} \right] (1+i) \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 $\15,000$ for the down payment for a house. What should be the size of the beginning-of-month payments if we have five years to save 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 a simple annuity due.

\begin{aligned} P &= PMT \left[ \frac{1-(1+i)^{-n}}{i} \right] (1+i) \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 $\45,000$ to purchase a new vehicle. We have agreed to make bi-weekly payments and the beginning of each payment period over the span of 10 years. If the rate remains constant at $6.5\%$ compounded bi-weekly, what should be the size of the equal-sized payments? Let’s work on this scenario in the following video.