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Another Way to Shop Around

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Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!
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THE SCENARIO Everyone's familiar with the concept of shopping around - you have an item you want, you look for it a bunch of different places, and you buy the item at the place with the cheapest price. However, for bigger-ticket items, there's more at play than just the price tag - unless you've got a boatload of cash, financing details affect the total amount you end up paying, and it can be valuable to put your energy into securing good financing rather than haggling over every last penny of the price. We'll do an example to see this concept in action, and we'll use a few assumptions when doing so.
  1. Everything will be 100% financed, so we're not going to worry about down payments
  2. There will be no costs to originate a loan
  3. The loans will be the same in all ways except for rate. They'll be 72-month, fully-amortizing loans.
The question: The question: Let's say I have the chance to buy a car and I've negotiated the price down to $40,000 and the loan I can get is at 5.5% (we'll call this the 'first loan'). But what if I wasn't able to haggle the price down as much, but I could negotiate a lower interest rate on the loan? If I could negotiate my interest rate down to 3.25% (we'll call this the 'second loan'), could I accept the higher price on the car but still save $1,000 overall? How much could I pay for the car in that situation?
THE SOLUTION This one has a few parts.
  1. Find out what my payment is with the first loan
  2. Find out the total I'm paying over the life of the first loan
  3. Find out how much I'm willing to pay for the second loan each month
  4. Find out the car's price under the second loan
First things first, make sure the calculator is using 12 Payments per Year. Part 1: First Loan's Payment N: 72 (The loan lasts for 72 months) I/YR: 5.5 (The first loan's rate is 5.5%) PV: 40,000 (With the first loan, I'm buying the car for $40,000) PMT: (This is what I'm trying to find) FV: 0 (The loan amortizes fully)

The monthly payment with the first loan is $653.52.

Part 2: The First Loan's Total The sum of all the payments to the first loan's lender is $653.52 x 72 = $47,053.11. Part 3: The Second Loan's Monthly Payment My goal in getting the second loan is to pay $1,000 less than the total payments under the first loan, so the total of its payments is $47,053.11 - $1,000 = $46,053.11. Since the second loan has 72 payments, that means that the monthly payment under the second loan is $46,053.11 ÷ 72 = $639.63. Part 4: Second Loan's Starting Balance N: 72 (The loan lasts for 72 months) I/YR: 3.25 (The second loan's rate is 3.25%) PV: (This is what I'm trying to find) PMT: -639.63 (From Part 3) FV: 0 (The loan amortizes fully)

The most I can borrow under the second loan is $41,789.88.

Note that by getting a lower interest rate, I can not only pay more for the car ($40,000 vs $41,789.88), but I'll pay less per month ($653.52 vs $639.63) which gets me that $1,000 discount I decided to make for myself from the start. Keep that in mind next time you're haggling over price - the loan terms can be at least as valuable to you as the number on the windshield.

What do you think? Have you ever neglected consideration of sale terms in favor of concentrating on the up-front price? Have you ever wondered why people concentrate so much on keeping their credit score high? Am I missing something here? Let us know in the comments!