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I have been considering purchasing a car. There are two methods I use to pay for it:

Method 1: The advertised price is $6,000 but there is a “Zero Percent Finance” offer that the shop has advertised, requiring to pay a 10% deposit followed by 18 monthly payments each of $300.

Method 2 Although the advertised price is $6,000, the salesman has indicated he might be willing to “do a deal” for only $5,400 if I can pay cash. My bank has agreed to lend me enough ($5,400) to purchase this TV and is offering me an 18-month loan with a fixed rate of 6% per annum. The loan is repayable in 18 equal monthly instalments.

How do I figure out which options work out to be cheaper? I think this involves annuity calculations? I worked out the second method to be $314.45 monthly payments after searching up a formula, but I'm not sure if it is right.

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    Are you buying a car or TV? The math doesn't change, but the advice you get likely will. – yoozer8 Mar 24 at 14:14
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    Have you verified that $600 up-front and the 18x$300 is exactly what you will pay with this financing arrangement? I've seen "zero percent interest" offers from car dealerships where the fine print says there is a monthly "finance charge" of $X per $1000 financed (not sure how this isn't "interest", but it worked out to be equivalent to at least a double-digit interest rate). – yoozer8 Mar 24 at 15:30
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    If this is a hypothetical situation, please say so. coursehero.com/tutors-problems/Financial-Accounting/… – Lou Mar 24 at 17:13
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    @Kevin Buying a $6000 television doesn't sound like a good idea to me. In fact, the existence of a $6000 television doesn't sound like a good idea either. – Ross Presser Mar 24 at 18:40
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    @Lou nailed it. That explains the Car vs TV typo. – TTT Mar 24 at 19:12
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Yes, the amount you have found seems to be right. If you add up these payments, you'll find out that you pay about $260 in interest, so in total your car will cost about $5660 instead of $6000 with the "0% finance".

For a better comparison, a payment of $600 out of your pocket (which you'd do on the first option as well) changes numbers: you'd only need a loan for $4800, paying $279.51 a month and $231 in total interest, making the product cost $5631.

And if you manage to pay off your loan earlier or can arrange a bigger downpayment, you'll save even more money in total.

(But, as a side note: Do you want to buy a car or a TV? For a car, this might be a reasonable price, a TV for $5400 seems a waste of money to me. But YMMV, of course.)

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    If one actually wants a $5000+ TV, I'd suggest they do it by paying cash, and only if they have money to burn. That had to be a slip, right? the 65" OLEDS are down below $2500. – JTP - Apologise to Monica Mar 24 at 10:23
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    Even more of waste of money for a TV if you have to borrow the money to pay for it. Users on this site sometimes debate whether borrowing money to buy a car is OK; I doubt anyone would advise borrowing $6000 to buy a TV. – yoozer8 Mar 24 at 14:17
  • @yoozer8 perhaps it's just barely permissible if you were already planning to save and buy it in a few months, and you now want to have a big party sooner than that – user253751 Mar 24 at 14:28
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tl;dr: The dealership is trying to offer you the equivalent of financing at a 13.6% interest rate, along with a nasty pre-payment penalty of all the remaining interest if you try to pay it off early.

Here is some general advice in how you should think about this. Note it isn't really the case that you're getting a discount if you pay in full up-front. Instead, $5400 is the actual price of the car, and you will be charged more if you choose to finance. Consider these 3 options:

  1. $5400 paid up front.
  2. $5400 financed for 18 months at 13.601%. The total paid after 18 months = $6000. (Hypothetical option for comparison.)
  3. $6000 financed for 18 months at 0%. Total paid after 18 months = $6000.

You are being offered #1 and #3, and at first glance #2 might seem like the same thing as #3. However, even though #2 is an awful rate right now, it's still much better than #3, because it gives you the opportunity to seek better financing through your own bank in the future (assuming there is no pre-payment penalty). Even if you didn't have your 6% financing ready to go, in your case you could refinance #2 within days or months after purchasing, lower your rate, and come out ahead. But with #3, you're stuck paying the full $6000 regardless if you have the ability to pay it off early or not.

Moral of the story: when presented with these options, you would prefer them in order: #1 over #2 over #3.

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  • Should option 2 be "$5400 financed for 18 months at 6%"? I'm confused. – stannius Mar 25 at 14:18
  • @stannius - No, not for the comparison I'm trying to make, which is that the dealership is offering #1 or #3 only. #2 is there to highlight how bad #3 really is. The paragraph below it explains that #2 can be replaced with 6% as you suggest. – TTT Mar 25 at 14:26
  • So #2 is a hypothetical option? – stannius Mar 25 at 14:28
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    @stannius - exactly. I edited for clarification. – TTT Mar 25 at 14:38
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    That looks much clearer, at least to me :) – stannius Mar 25 at 22:43
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The method you used is the correct method: calculate how much each option will cost you in advance.

From the dealer you will need $600 now, and be able to afford $300 a month for 18 months. The total cost will be $6,000

From the bank you will need nothing now, but you have to be able to afford $314.45 for 18 months. The total cost is $5,660. Of course if you can afford $600 now the loan will be that much lower, and the monthly payment will be lower also.

This is why you go to your bank or credit union first, and get approved for a loan. That means you know the total cost of that option before you walk into the dealership. Many times a car dealer can offer a zero percent finance option, or a better price. Which can allow you to get a loan from the bank, and pay the lower price for the car.

Getting approved in advance still gives you the option to take dealer financing if that method turns out to have the lower total cost.

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