# How does a mortgage work?

A mortgage is one of the biggest commitments you can make. Check out the nuts and bolts of what it really is, and how it works.

#### Transcript

What I want to do with this video is explain what a mortgage is, but I think most of us have a least a general sense of it. But even better than that, actually go into the numbers and understand a little bit of what you are actually doing when you're paying a mortgage, what it's made up of and how much of it is interest versus how much of it is actually paying down the loan. So, let's just start with a little example.

Let's say that there is a house that I like, let's say that that is the house that I would like to purchase. It has a price tag of, let's say that I need to pay $500,000 to buy that house, this is the seller of the house right here. And they have a mustache, that's the seller of the house. I would like to buy it. I would like to buy the house. This is me right here. And I've been able to save up $125,000. I've been able to save up $125,000 but I would really like to live in that house so I go to a bank, I go to a bank, get a new color for the bank, so that is the bank right there. And I say, Mr. Bank, can you lend me the rest of the amount I need for that house, which is essentially $375,000? I'm putting 25 percent down, this right, this right, this number right here, that is 25 percent of $500,000. So, I ask the bank, can I have a loan for the balance? Can I have a $375,000 loan? And the bank says, sure, you seem like, uh, uh, a nice guy with a good job who has a good credit rating. I will give you the loan but while you're paying off the loan you can't have the title of that house. We have to have that title of the house and once you pay off the loan we're going to give you the title of the house.

So what's going to happen here is we're going to have the loan is going to go to me, so it's $375,000, $375,000 loan. Then I can go and buy the house, so I'm going to give the total of $500,000, $500,000 to the seller of the house and I'll actually move into the house myself, assuming I'm using it for my own residence. But the title of the house, the document that says who actually owns the house, so this is the home title, this is the title of the house, home, home title. It will not go to me. It will go to the bank, the home title will go from the seller, maybe even the seller's bank, maybe they haven't paid off their mortgage, it will go to the bank that I'm borrowing from. And this transferring of the title to secure a loan, I say secure a loan, I'm saying, look, I need to give something to the lender in case I don't pay back the loan or if I just disappear. So, this is the security right here. That is technically what a mortgage is.

This pledging of the title for, as the, as the security for the loan, that's what a mortgage is. And actually it comes from old French, mort, means dead, dead, and the gage, means pledge, I'm, I'm a hundred percent sure I'm mispronouncing it, but it comes from dead pledge. Because, I'm pledging it now but that pledge will eventually die once I pay off the loan. Once I pay off the loan this pledge of the title to the bank will die, it'll come back to me. And that's why it's called a dead pledge or a mortgage. And probably because it comes from old French is the reason why we don't say mortgage. We say, mortgage.

But anyway, this is a little bit technical but normally when people refer to a mortgage they're

really referring to the loan itself. They're really referring to the mortgage, mortgage, the mortgage loan. And what I want to do in the rest of this video is use a little screenshot from a spreadsheet I made to actually show you the math or actually show you what your mortgage payment is going to. And you can download, you can download this spreadsheet at Khan Academy, khanacademy.org/downloads, downloads, slash mortgage calculator, mortgage, or actually, even better, just go to the download, just go to the downloads, downloads, uh, folder on your web browser, you'll see a bunch of files and it'll be the file called mortgage calculator, mortgage calculator, calculator dot XLSX. So, it's a Microsoft 2007 format. But just go to this URL and then you'll see all of the files there and then you can just download this file if you want to play with it. But what it does here is in this kind of dark brown color, these are the assumptions that you could input and that you can change these cells in your spreadsheet without breaking the whole spreadsheet.

So, here I would assume the 5.5 percent interest rate. I'm buying a $500,000 home. It's a 25 percent down payment, so that's the $125,000 that I had saved up, that I'd talked about right over there. And then the, uh, loan amount, well, I have the $125,000, I'm going to have to borrow $375,000. It calculates it for us and then I'm going to get a pretty plain vanilla loan. This is going to be a 30-year, so when I say term in years, this is how long the loan is for. So, 30 years, it's going to be a 30-year fixed-rate mortgage, fixed-rate, fixed-rate, which means the interest rate won't change. We'll talk about that in a little bit. This 5.5 percent that I am paying on my, on the money that I borrowed will not change over the course of the 30 years. We will see that the amount I borrowed changes as I pay down some of the loan.

Now, this little tax rate that I have here, this is to actually figure out, what is the tax savings of the interest deduction on my loan? And we'll talk about that in a second, we can ignore it for now. And then these other things that aren't in brown, you shouldn't mess with these if you actually do open up this spreadsheet yourself. These are automatically calculated and this right here is a monthly interest rate. So, it's literally the annual interest rate, 5.5 percent, divided by 12 and most mortgage loans are compounded on a monthly basis. So, at the end of every month they see how much money you owe and then they will charge you this much interest on that for the month.

Now, given all of these assumptions, there's a little bit of behind the scenes math and in a future video I might actually show you how to calculate what the actual mortgage payment is. It's actually a pretty interesting problem. But for a $500,000 loan, well, a $500,000 house, a $375,000 loan over 30 years at a 5.5 percent interest rate. My mortgage payment is going to be roughly $2,100.

Now, right when I bought the house I want to introduce a little bit of vocabulary and we've talked about this in some of the other videos. There's an asset in question right here, it's called

a house. And we're assuming that it's worth $500,000. We are assuming that it's worth $500,000. That is an asset. It's an asset because it gives you future benefit, the future benefit of being able to live in it. Now, there's a liability against that asset, that's the mortgage loan, that's the $375,000 liability, $375,000 loan or debt.

So, if you are, if this was your balance sheet. If this was all of your assets and this is all of your debt and if you were essentially to sell the assets and pay off the debt. If you sell the house you'd get the title, you can get the money and then you pay it back to the bank. Then, well actually, it doesn't necessarily go into that order but I won't get too technical. But if you were to unwind this transaction immediately after doing it then you would have, you would have a $500,000 house, you'd pay off your $375,000 in debt and you would get in your pocket $125,000, which is exactly what your original down payment was but this is your equity. And the reason why I'm pointing it out now is I'm, in this video I'm not going to assume anything about the house price, whether it goes up or down, we're assuming it's constant. But you could not assume it's constant and play with the spreadsheet a little bit. But I, what I would, I'm introducing this because as we pay down the debt this number is going to get smaller.

So, this number is getting smaller, let's say at some point this is only $300,000, then my equity is going to get bigger. So, you can kind of view equity as how much value do you have after you pay off the debt for your house? If you were to sell the house, pay off the debt, what do you have left over for yourself? So, this is really kind of your, this is the real wealth in the house, the owner is, this is what you own, wealth in house or the actual what the owner has. Now, what I've done here is, well, actually before I get to the chart, let me actually show you how I calculate the chart and I do this over the course of 30 years and it goes by month.

So, so you can imagine that there's actually 360 rows here on the actual spreadsheet and you'll see that if you go and open it up. But I just want to show you what I did. So, on month zero, which I don't show here, you borrowed $375,000. Now, over the course of that month they're going to charge you 0.46 percent interest, remember that was 5.5 percent divided by 12. 0.46 percent interest on $375,000 is $1,718.75. So, I haven't made any mortgage payments yet. So, I've borrowed $375,000, this much interest essentially got billed up on top of that, it got accrued. So, now before I pay any of my payments, instead of owing $375,000 at the end of the first month I owe $376,718.

Now, I'm a good guy, I'm not going to default on my mortgage so I make that first mortgage payment that we calculated, that we calculated right over here. So, after I make that payment then I'm essentially, what's my loan balance after making that payment? Well, this was before making the payment so you subtract the payment from it, this is my loan balance after the payment.

Now, this right here, what I, little asterisk here, this is my equity now. So, remember, I started with $125,000 of equity. After paying one loan balance, after, after my first payment I now have $125,410 in equity. So, my equity has gone up by exactly $410. Now, you're probably saying, hey, gee, I made a $2,000 payment, a roughly a $2,000 payment and my equity only went up by $410. Shouldn't this debt have gone down by $2,000 and my equity have gone up by $2,000? And the answer is no, because you had to pay off all of this interest, all of this interest. So, that very, in the beginning, your payment, your $2,000 payment is mostly interest. Only $410 of it is principal. But as you, and then you, and then, so as your loan balance goes down you're going to pay less interest here and so each of your payments are going to be more weighted towards principal and less weighted towards interest. And then to figure out the next line, this interest accrued right here, I took my, your old, your loan balance exiting the last month multiply that times 0.46 percent and you get this new interest accrued. This is your new prepayment balance. I pay my mortgage again. This is my new loan balance. And notice, already by month two, $2.00 more went to principal and $2.00 less went to interest. And over the course of 360 months you're going to see that it's an actual, sizable difference. And that's what this chart shows us right here. This is the interest and principal portions of our mortgage payment.

So, this entire height right here, this is, let me scroll down a little bit, this is by month. So, this entire height, if you notice, this is the exact, this is exactly our mortgage payment, this $2,129. Now, on that very first month you saw that of my $2,100 only $400 of it, this is the $400, only $400 of it went to actually pay down the principal, the actual loan amount. The rest of it went to pay down interest, the interest for that month. Most of it went for the interest of the month. But as I start paying down the loan, as the loan balance gets smaller and smaller, each of my payments, there's less interest to pay, let me do a better color than that. There is less interest, let's say if we go out here, this is month 198, over there that last month there was less interest so more of my $2,100 actually goes to pay off the loan. Until we get all the way to month 360 and you can show, see this in the actual spreadsheet, at month 360 my final payment is all going to pay off the principal, very little if anything of that is interest.

Now, the last thing I want to talk about in this video without making it too long is this idea of an interest tax deduction. So, a lot of times you'll hear financial planners or realtors tell you, hey, the benefit of buying your house is that it, it's, it has tax advantages, and it does. Your interest is tax-deductible. Your interest, not your whole payment. Your interest is tax deductible, deductible. And I want to be very clear with what deductible means. So, let's for instance, talk about the interest fees.

So, this whole time over 30 years I am paying $2,100 a month or $2,129.29 a month. Now, at the beginning a lot of that is interest. So, on month one, $1,700 of that was interest. That $1,700 is tax-deductible. Now, as we go further and further each month I get a smaller and smaller tax-deductible portion of my actual mortgage payment. Out here the tax deduction is

actually very small. As I'm getting ready to pay off my entire mortgage and get the title of my house. Now, I want to be very clear on this notion of what tax-deductible even means ‘cause I think it is misunderstood very often. This doesn't mean, let's say that, let's say in one year, let's say in one year I paid, I don't know, I'm going to make up a number, I didn't calculate it on the spreadsheet.

Let's say in year one, year one, I pay, I pay $10,000 in interest, $10,000 in interest. Remember, my actual payments will be higher than that because some of my payments went to actually paying down the loan. And, but let's say $10,000 went to interest. To say this deductible, and let's say before this, let's say before this I was making $100,000. Let's put the loan aside, let's say I was making $100,000 a year and let's say I was paying roughly 35 percent on that $100,000. I won't go into the whole, uh, tax structure and the, and the different brackets and all of that. Let's say, you know, if I didn't have this mortgage I would pay 35 percent taxes which would be about $35,000 in taxes for that year. Just, this is just a rough estimate. Now, when you say that $10,000 is tax-deductible, the interest is tax-deductible, that does not mean that I can just take it from the $35,000 that I would have normally owed and only paid $25,000. What it means is, I can deduct this amount from my income. So, when I tell the IRS how much did I make this year, instead of saying, I made $100,000 I say that I made $90,000 because I was able to deduct this, not directly from my taxes, I was able to deduct it from my income.

So, now if I only made $90,000 and I, and this is I'm doing a gross oversimplification of how taxes actually get calculated. And I paid 35 percent of that, let's get the calculator out. Let's get the calculator. So, 90 times .35 is equal to $31,500. So, this will be equal to $31,500, put a comma here, $31,500. So, off of a $10,000 deduction, $10,000 of deductible interest, I essentially saved $3,500. I did not save $10,000. So, another way to think about it if I paid $10,000 interest, I'm going to, and my tax rate is 35 percent, I'm going to save 35 percent of this in actual taxes.

This is what people mean when they say deductible. You're deducting it from the income that you report to the IRS. If there's something that you could actually take straight from your taxes, that's called a tax credit. So, if you were, uh, if there was some special thing that you could actually deduct it straight from your credit, from your taxes, that's a tax credit, tax credit. But a deduction just takes it from your income. And so, in this spreadsheet I just want to show you that I actually calculated in that month how much of a tax deduction do you get.

So, for example, just off of the first month you paid $1,700 in interest of your $2,100 mortgage payment. So, 35 percent of that, and I got the 35 percent as one of your assumptions, 35 percent of $1,700. I will save $600 in taxes on that month. So, roughly over the course of the first year I'm going to save about $7,000 in taxes, so that's nothing, nothing to sneeze at.

Anyway, hopefully you found this helpful and I encourage you to go to that spreadsheet and, uh, play with the assumptions, only the assumptions in this brown color unless you really know what you're doing with the spreadsheet. And you can see how the, this actually changes based on different interest rates, different loan amounts, different down payments, different terms, different tax rates, that'll actually change the, the tax savings and you can play around with the different types of fixed mortgages on this spreadsheet.

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