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# Introduction to mortgage loans

Learn how mortgages work, how to use a mortgage calculator, and how to use a spreadsheet to show the payoff of a mortgage over time and the interest paid each year. Click here to download the spreadsheet from the video. Created by Sal Khan.

## Video transcript

- [Voiceover] What I
want to do in this video is explain what a mortgage is. I think most of us have at
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. 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 dollars. 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, let me get
a good color for a bank. 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% down.
This number right here, that is 25% of $500,000. So I ask the bank, "Can I
have a loan for the balance? Can I have $375,000 loan?" And the bank says, "Sure.
You seem like a nice guy "with a good job who
has 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." What's gonna happen here is
the loan is gonna go to me, so it's $375,000. $375,000 loan. Then I can go and buy the house. I'm gonna give the total $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. This is the home title. This is the title of the house. Home title. It will not go to me.
It will go to the bank. The home title will go from the seller, or maybe even the seller's bank, because maybe they haven't
paid off their mortgage. It will go to the bank
that I'm borrowing from. This transferring of the
title to secure a loan. When I say "secure a
loan," I'm saying I need to give something to the
lender in case I don't pay back the loan or if I just disappear. This is the security right here. That is technically what a mortgage is. This pledging of the title
as the security for the loan, that's what a mortgage is. It actually comes from old French. Mort means dead, and
the gage means pledge. I'm 100% 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 and it will come back to me. That's why it's called a
dead pledge, or a mortgage. And probably because it
comes from old French is the reason we don't say
mort-gage, 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 loan. What I want to do in
the rest of this video is use a screenshot from
a spreadsheet I made to actually show you the math, or actually show you what your
mortgage payment is going to. You can download this
spreadsheet at khanacademy, khanacademy.org/downloads/mortgagecalculator Or actually, even better, just
go to the downloads folder and on your web browser
you'll see a bunch of files, and it will be the file
called MortgageCalculator, MortgageCalculator.xlsx. It's a Microsoft 2007 format. Just go to this URL, then
you'll see all the files there and you can just download this file if you want to play with it. What it does here, in this
kind of dark brown color, these are the assumptions
that you can input and then you can change these
cells in your spreadsheet without breaking the whole spreadsheet. Here I've assumed a 5.5% interest rate. I'm buying a $500,000 home. It's a 25% down payment, that's the $125,000 that I had saved up, that I talked about right over there. And then the loan amount. Well, I have 125, I'm
gonna have to borrow 375, it calculates it for us. And then I'm gonna get a
pretty plain vanilla loan. This is gonna be a 30 year. When I say term in years, this
is how long the loan is for. So 30 years. It's gonna be a 30 year
fixed-rate mortgage. Fixed rate, which means the
interest rate won't change. We'll talk about that a little bit. This 5.5% that I'm paying
on the money that I borrowed will not change over the
course of the 30 years. We will see that the amount I've borrowed changes as I pay down some of the loan. 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. We'll talk about that in a second, you can ignore it for now. Then these other things
that aren't in brown, you shouldn't mess with these if you actually do open up the
spreadsheet yourself. These are automatically calculated. This right here is a
monthly interest rate. So it's literally the
annual interest rate, 5.5%, 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 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% interest rate, my mortgage payment is
going to be roughly $2,100. 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 a asset in question
right here, it's called a house. And we're assuming it's worth $500,000. We're assuming 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 a $375,000 liability. $375,000 loan or debt. If this was your balance sheet, if this was all of your assets
and this is all of your debt, and you were essentially
to sell the assets and pay off the debt, if you sell the house you get the title, you can get the money, then
you pay it back to the bank. 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 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. The reason why I'm pointing it out now is, in this video I'm not
gonna 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'm introducing this
because as we pay down the debt this number's 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 could do equity is
how much value 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. This is the real wealth in the
house, this is what you own. Wealth in house, or the
actual what the owner has. What I've done here is-- Actually before I get to
the chart let me actually show you how I calculate the chart. I do this over the course of
30 years, and it goes by month. So you can imagine that there's actually 360 rows here in 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. On month 0, which I don't show
here, you borrow $375,000. Now, over the course of that month they're going to charge you .46% interest. Remember, that was 5.5% divided by 12. .46% interest on $375,000 is $1,718.75. So I haven't made any
mortgage payments yet. I've borrowed 375,000. This much interest essentially
got built up on top of that, it got accrued. So now before I've paid
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
gonna default on my mortgage so I make that first mortgage payment that we calculated right over here. 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, the
little asterisk here, this is my equity now. So remember, I started
with $125,000 of equity. After paying one loan balance,
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,
"Gee. I made a $2,000 payment, "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 all of this interest. So at the very beginning, your payment, your $2,000 payment, is mostly interest. Only $410 of it is principal. So as your loan balance goes down you're going to pay less interest here, 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 your loan balance
exiting the last month, multiplied that times .46%. You get this new interest accrued. This is your new pre-payment balance. I pay my mortgage again.
This is my new loan balance. And notice, already by month
two, $2 more went to principal. and $2 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, you notice, 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's less interest. 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. You can 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 a interest tax deduction. A lot of times you'll hear
financial planners or realtors tell you the benefit of buying your house is it has tax advantages, and it does. Your interest is tax deductible. Your interest, not your whole payment. Your interest is tax deductible. I want to be very clear
what deductible means. First let's talk about
what the interest means. This whole time over 30 years
I am paying $2,100 a month, or $2129.21 a month. Now the beginning, a
lot of that is interest. So on month one, 1,700
of that was interest. That $1,700 is tax deductible. As we go further and further, each month I get 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. I want to be very clear on this notion of what tax deductible even means, because I think it is
misunderstood very often. Let's say in one year
I paid, I don't know, I'm gonna make up a number, I didn't calculate it on the spreadsheet. Let's say in year one 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. But let's say 10,000 went to interest. 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% on that 100,000. I won't go into the whole tax structure and the different
brackets and all of that. Let's say if I didn't have this mortgage I would pay 35% taxes, which would be about $35,000
in taxes for that year. This is just a rough estimate. 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 pay 25,000. What it means is I can deduct
this amount from my income. 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 this is, I'm doing a
gross oversimplification of how taxes actually get calculated -- and I pay 35% 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. $31,500. Off of a 10,000 deduction,
$10,000 of deductible interest, I essentially saved $3,500.
I did not save $10,000. Another way to think about it, if I paid 10,000 interest
and my tax rate is 35%, I'm gonna save 35% 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 take straight from your taxes, that's
called a tax credit. If there was some special
thing that you could actually deduct it straight from your
taxes, that's a tax credit. But a deduction just
takes it from your income. On 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% of that, and I got 35%
as one of your assumptions, 35% of $1,700, I will save
$600 in taxes on that month. So roughly over the
course of the first year I'm gonna save about $7,000 in taxes, so that's nothing to sneeze at. Anyway, hopefully you found this helpful and I encourage you to
go to that spreadsheet, and play with the assumptions, only the assumptions in this brown color unless you really know what
you're doing with a spreadsheet, and you can see how this
actually changes based on different interest rates,
different loan amounts, different down payments, different terms. Different tax rates, that will actually change the tax savings, and you can play around
with the different types of fixed mortgages on this spreadsheet.