Because it is feeling unsafe to check into random hotels, my wife would like us to buy a Recreational Vehicle (RV; it's basically a box on wheels with beds inside, that you can pull using your car) this Summer, and travel with it. We found an RV we sort of like, and we inquired about the price, which was $21,000. That is over our budget, so we naturally started to bargain with the RV dealer. His first response was that if we borrow money from them to finance our purchase, he will drop $1,000 from the price, and sell it to us for $20,000. This is because they have a deal with a bank, but the catch is that I have to maintain the loan for 9 months at least. My rate of interest would have been 7%, compounded monthly. Here's how this would work:

1. First, imagine this is an annuity, and the terms of the loan are 180 months. Every month, you would pay back a fixed amount, some of which would be interest payments, while the rest are principal payments.

2. Because I do not want to pay over $10,000 in interest by keeping this 180-month loan, they will allow me to make one huge payment in month one, that is equal to the principal (20,000) minus 8 monthly payments of the annuity. That is, if the fixed amount paid each month was (just for the purpose of an example!) $200, I would be allowed to pay 20,000 - 8x200 = $18,400.

3. Of that large payment, some would go to interest, some to the principal (quite a lot to the principal!). So now, I am left with a much smaller principal, that I have to pay back in 8 months, at the same interest rate. Over this time, I will pay some interest, of course.

I want to calculate the total amount of interest I will have to pay under this unusual 9-month loan, in order to compare it with the $1,000 discount.

Rounding to $10, the total amount of interest and my conclusion will be:

		$160 and the 9-month loan is a good deal
		$380 and the 9-month loan is a good deal
		$810 and the 9-month loan is not a good deal
		$1,240 and the 9-month loan is not a good deal