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Hi.
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In this problem, john wants to buy a car, a honda.
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And in order to buy it, he puts $3 ,000 down, and then he pays $450 a month at the end of each month for four years.
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We're given that interest is compounded monthly at 4 .9%.
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And we're asked to find the cost of the honda.
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So you might have realized this now, but so the kind of the hardest part of this problem is to figure out which which formula to use.
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So there's two things we're considering.
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The first one is present versus future value.
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And then the second thing is annuity.
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Do we want do? or do we want ordinary? so the first thing that we'll talk about is the annuity, because it's actually the more simple one.
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So in this case, do versus ordinary, all it means is when you make your, regular payments.
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Ordinary is at the beginning of each period and due is at the end.
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And we know that we're paying at the end of each month.
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So we want annuity due.
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Now for present versus future value, it's a little more a little bit more subtle.
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So present value says how much given that you're going to make all these investments, how much would you have to put right now for it to be the same at the end after the end of the four years? whereas future value says how much your money is going to be worth in four years after you've put it all down.
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So what we're going to use because what we want to say is, well, let's say john had enough money to buy the honda right now in cash, just everything right now, how much would it cost? and so what that is is the present value.
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So it's saying, well, given interest rates, you have to pay a little bit each month.
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But so if you had enough money right now, what would it cost? so that's the present value...