# Installment Purchases: Payment & Terms

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how installment purchases work. Learn how you can calculate the amount of your fixed installment payment.

## Installment Purchase

Some companies will sell you something that costs quite a bit of money and let you make an installment purchase. This kind of purchase lets you pay for the item in several future payments. You get to enjoy the item while you pay for it.

You might see an advertisement for a knife set where you pay just four payments of \$59.95. Installment purchases can be simple like that knife set or they can be more complicated. That all depends on the kinds of terms involved. Some installment purchases will have interest included while others won't.

## Terms

The terms are the conditions of the installment purchase. They tell you what kinds of payments to expect and when you need to pay them. For the knife set, our terms are very simple. All we need to do is to make 4 monthly payments of \$59.95 and we are done. There is no interest mentioned here. These are simple terms.

More complicated terms may have an interest payment involved. They might say that you need to make monthly payments for 5 years and also pay an annual interest of 5%. These more complicated terms are for much larger purchases, such as a car costing you \$20,000.

## Formula

Because there is an interest involved in our terms now, our monthly payment won't be the cost of our car divided by the number of months. We also have to include the interest payment. Good thing for us math learners, we have a formula that allows us to calculate our fixed monthly:

Here, P stands for our fixed monthly payment, L stands for the cost of the item, r stands for the interest rate, and n the total number of payments. To use this formula, we plug in our values for L, r, and n to calculate our P.

## Example

Let's use this formula to calculate our monthly payments for our car that costs \$20,000.

Note that if n is yearly, then r will be the annual interest rate. If n is monthly, then r will be the monthly interest rate or the annual interest rate divided by 12.

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