# Deferred Payment vs. Cash Price: Calculation & Interest

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• 0:02 The Problem
• 1:00 Cash Price
• 1:47 Deferred Payment
• 2:38 Calculating Interest
• 4:36 Lesson Summary
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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.

Watch this video lesson to learn the difference between paying cash up front for an item versus making payments at a later time for an item. Watch and see how you may end up paying more for an item if you pay later.

## The Problem

The big game is going to be on TV in just a few weeks. You are planning a big party for all your friends to come over and cheer on your favorite team. But, right now, your TV isn't large enough for the number of friends you want to invite. So, you take yourself to the local department store to look for some televisions.

You walk through the TV section, and you see this giant big screen TV for sale. This is perfect! The price? Not so perfect. Its original price is \$1,000, but it's on sale today for \$600. That's a savings of \$400! That's a good deal. But, do you have \$600 laying around waiting for you to spend it? Well, you would if you asked your friends to chip in. But, by yourself, you don't really have that much you can spend.

What do you do? You take the television and you ask to speak with the manager at the store to see what kinds of buying options you have. The manager begins with giving you the most common option and the preferred option for his store.

## Cash Price

This option is where you pay cash price for the item, meaning you pay the full price of the item up front. This is the option that you are using most times when you go shopping. You pay for the item, and then you get to take it home and use it.

With this option, the price you see is the price you pay, plus any taxes or fees involved depending on where you live. In California, for example, the sales tax is different in each county and possibly different in different cities plus you have an electronics disposal fee that you pay when you purchase electronics. These costs are in addition to the listed price you see. So, your TV has a cash price of \$600 plus sales tax and applicable fees.

## Deferred Payment

The next option that the manager talks to you about is the deferred payment option. This option lets you pay for the item at a later date. For this TV, you can either pay the full price of the item within 6 months, or you can make smaller payments after 6 months until you finish paying for the item. The only thing about making the smaller payments is that you also have to pay interest on the amount you still owe the store.

You can't make just any payment amount you want, though. The store wants you to pay for the item in 12 monthly payments. If you divide \$600 by 12, you get a monthly payment of \$50 plus any interest involved. The interest, the store manager tells you that the store charges, is 10% annually.

This option sounds the best to you. You do have \$50 you can spend each month. But, what about the interest? How much will that be? You need to make some calculations so you can say for sure that you will take this option.

## Calculating Interest

Because you are paying \$50 each month, your interest each month will change because your monthly balance keeps decreasing. First, we need to calculate the monthly interest. To do this, we divide the annual interest by the number of months, by 12. We get 0.1/12 = 0.00833.

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