Introduction to interest | Interest and debt | Finance & Capital Markets | Khan Academy


Well now you’ve learned what I
think is quite possibly one of the most useful concepts in
life, and you might already be familiar with it, but if you’re
not this will hopefully keep you from one day filing
for bankruptcy. So anyway, I will talk about
interest, and then simple versus compound interest. So what’s interest? We all have heard of it. Interest rates, or interest
on your mortgage, or how much interest do I owe
on my credit card. So interest– I don’t know what
the actual formal definition, maybe I should look it up
on Wikipedia– but it’s essentially rent on money. So it’s money that you pay
in order to keep money for some period of time. That’s probably not the most
obvious definition, but let me put it this way. Let’s say that I want to
borrow $100 from you. So this is now. And let’s say that this
is one year from now. One year. And this is you,
and this is me. So now you give me $100. And then I have the $100
and a year goes by, and I have $100 here. And if I were to just give you
that $100 back, you would have collected no rent. You would have just
got your money back. You would have
collected no interest. But if you said, Sal I’m
willing to give you $100 now if you give me $110 a year later. So in this situation, how
much did I pay you to keep that $100 for a year? Well I’m paying you
$10 more, right? I’m returning the $100, and
I’m returning another $10. And so this extra $10 that I’m
returning to you is essentially the fee that I paid to be able
to keep that money and do whatever I wanted with that
money, and maybe save it, maybe invest it, do
whatever for a year. And that $10 is
essentially the interest. And a way that it’s often
calculated is a percentage of the original amount
that I borrowed. And the original amount that I
borrowed in fancy banker or finance terminology is
just called principal. So in this case the rent on the
money or the interest was $10. And if I wanted to do it as a
percentage, I would say 10 over the principal– over 100–
which is equal to 10%. So you might have said, hey Sal
I’m willing to lend you $100 if you pay me 10% interest on it. So 10% of $100 was $10, so
after a year I pay you $100, plus the 10%. And likewise. So for any amount of money, say
you’re willing to lend me any amount of money for
a 10% interest. Well then if you were to lend
me $1,000, then the interest would be 10% of that,
which would be $100. So then after a year I would
owe you $1,000 plus 10% times $1,000, and that’s
equal to $1,100. All right, I just added
a zero to everything. In this case $100 would
be the interest, but it would still be 10%. So let me now make a
distinction between simple interest and compound interest. So we just did a fairly simple
example where you lent money for me for a year at
10% percent, right? So let’s say that someone were
to say that my interest rate that they charge– or the
interest rate they charge to other people– is– well 10% is
a good number– 10% per year. And let’s say the principal
that I’m going to borrow from this person is $100. So my question to you– and
maybe you want to pause it after I pose it– is how
much do I owe in 10 years? How much do I owe in 10 years? So there’s really two ways
of thinking about it. You could say, OK in years at
times zero– like if I just borrowed the money, I just
paid it back immediately, it’d be $100, right? I’m not going to do that,
I’m going to keep it for at least a year. So after a year, just based on
the example that we just did, I could add 10% of that amount to
the $100, and I would then owe $110. And then after two years, I
could add another 10% of the original principal, right? So every year I’m
just adding $10. So in this case it would be
$120, and in year three, I would owe $130. Essentially my rent per year to
borrow this $100 is $10, right? Because I’m always taking
10% of the original amount. And after 10 years– because
each year I would have had to pay an extra $10 in interest–
after 10 years I would owe $200. Right? And that $200 is equal to $100
of principal, plus $100 of interest, because I paid
$10 a year of interest. And this notion which I just
did here, this is actually called simple interest. Which is essentially you take
the original amount you borrowed, the interest rate,
the amount, the fee that you pay every year is the interest
rate times that original amount, and you just
incrementally pay that every year. But if you think about it,
you’re actually paying a smaller and smaller percentage
of what you owe going into that year. And maybe when I show
you compound interest that will make sense. So this is one way to interpret
10% interest a year. Another way to interpret it is,
OK, so in year zero it’s $100 that you’re borrowing, or if
they handed the money, you say oh no, no, I don’t want it and
you just paid it back, you’d owe $100. After a year, you would
essentially pay the $100 plus 10% of $100,
right, which is $110. So that’s $100,
plus 10% of $100. Let me switch colors,
because it’s monotonous. Right, but I think this
make sense to you. And this is where simple
and compound interest starts to diverge. In the last situation we
just kept adding 10% of the original $100. In compound interest now,
we don’t take 10% of the original amount. We now take 10% of this amount. So now we’re going
to take $110. You can almost view it
as our new principal. This is how much we offer
a year, and then we would reborrow it. So now we’re going to owe
$110 plus 10% times 110. You could actually undistribute
the 110 out, and that’s equal to 110 times 110. Actually 110 times 1.1. And actually I could
rewrite it this way too. I could rewrite it as
100 times 1.1 squared, and that equals $121. And then in year two, this is
my new principal– this is $121– this is my
new principal. And now I have to in year
three– so this is year two. I’m taking more space,
so this is year two. And now in year three, I’m
going to have to pay the $121 that I owed at the end of year
two, plus 10% times the amount of money I owed going
into the year, $121. And so that’s the same thing–
we could put parentheses around here– so that’s the same thing
as 1 times 121 plus 0.1 times 121, so that’s the same
thing as 1.1 times 121. Or another way of viewing it,
that’s equal to our original principal times 1.1
to the third power. And if you keep doing this–
and I encourage you do it, because it’ll really give you a
hands-on sense– at the end of 10 years, we will owe– or you,
I forgot who’s borrowing from whom– $100 times 1.1
to the 10th power. And what does that equal? Let me get my spreadsheet out. Let me just pick a random cell. So plus 100 times 1.1
to the 10th power. So $259 and some change. So it might seem like a very
subtle distinction, but it ends up being a very big difference. When I compounded it 10% for
10 years using compound interest, I owe $259. When I did it using simple
interest, I only owe $200. So that $59 was kind of the
increment of how much more compound interest cost me. I’m about to run out of time,
so I’ll do a couple more examples in the next video,
just you really get a deep understanding of how to do
compound interest, how the exponents work, and what
really is the difference. I’ll see you in the next video.

99 thoughts on “Introduction to interest | Interest and debt | Finance & Capital Markets | Khan Academy

  1. It's like money making kids. But money isn't alive. Money shouldn't be able to make kids… I think this is why our economic system goes wrong…

  2. because every year you get 10% interest, meaning the final total of every year is 110/100 which 1.1.

    So with your principal at 100, with 10% interest in mind it is 110/100 x 100 = 110. For the second year you can either calculate it by 110/100 x 110 or (110/100)^2 x 100

  3. I hear clearly, and after watching all of his videos up to this point in order, it completely makes sense that he would say that. Watch the series on compound interest and the number e and you'll see as well that it's true. If you don't I don't expect you to be arguing anymore since you would be arguing with lack of knowledge.

  4. I'm watching them in upload order I would have never known about that video if that were true. Like I said if you don't watch it, then keep your arguments to yourself. And don't make up lies to justify your argument.

  5. If you are referring to 5:45 no. This is what you owe overall. 1st year- $110 2nd year- $120 etc. You do not pay that at the end of the year, that's how much you owe. Your principal is multiplied by .1 every year (which is the interest rate, 10%) until you pay the principal.

  6. Actually I believe he did say "now you've learned" I think he was referring to the Binomial Theorem. Look at his Pre-Calculus playlist, this is video 17 out of 44 in the playlist.

  7. Thank you so much! I owe you a big part of my studies! Whenever I do not understand economics, statistics, math of finance, you are the one who helps me understand. So I wanted to say thank you!! You are an amazing Professor! Again very very thankful! 🙂

  8. Hello I stumbled upon this video when I was looking for your Share market and Stock and Options related videos, I could not find them anywhere on the channel . Can you help me locate the course or playlist. Thanks,

  9. Really? Why don't you teach it to the person who filed for bankruptcy four times then? And still thinks he's a "winner" because other people who work with money manage it for him.

  10. You could also teach it to people at Wells Fargo. I had a friend who dropped them cold over 5 years ago because she thought they were "the worst financial institution ever." She withdrew everything and told everyone who would listen about how they were the worst financial institution ever.

  11. There's a formula for simple interest: A=P(1+it) You learn this for the Actuarial FM Exam. A is amount value, P is the principal, i is the interest rate, and t is time. Compound would be A=P(1+i)^t

  12. Funny everyone programmed to accept this interest idea the way it is. You see how the loan shark got $200 from $100 loan? He made $100 for doing nothing. No one else is benefiting 200% from this transaction. If the loan was to buy a bike, the bike manufacture got paid for just 1 bike. The owner received 1 bike. Yet the loan shark get paid for 2 bikes……hmmmm ok great system that no one dares to question.

  13. They call it interest because people have no interest in loaning money for nothing. But the idea of receiving money on top of the money that they loaned makes the offer much more interesting.

  14. I wished sal would have used a new car loan as an example. Most car loans use simple interest thus making the illustration more practical. In his example sal is assuming the principle doesnt change, someone borrows $100 @ 10% interest and waiting x number of years to pay it back. No one does this most people will make subsequent payments over time thus reducing the principle.

  15. but why am i taught to use i=prt instead? with that formula we would jist compute the actual money with the interest… then we wouldnt really be getting the interest unless we subtract it to the principal money, right? but if we really want to get the interest asap we should just use i=prt. then again when looking for the actual money with its interest, we can use p(1+tr).

  16. in simple interest rate, after each year it should be 110 dollars. same because principle is same and interest is also same

  17. i swear this is how i had explained to myself, 'rent on money'! im 32 years old noob in finance…thats why sal hits the mark for even the uninitiated!

  18. I have two questions, can somebody give me an idea please? suppose we have two companies in an industry i.e. 1) ABC 2) DEF. Let's say we have financial reports of both companies for 5 years. For each company i can find all the ratios for every year separately. suppose we are going to find a specific ratio i.e. liquidity ratio of both companies.
    Now my questions are: 1) How to find combined liquidity ratio for company ABC for 5 years?
    2) How we can calculate combined liquidity ratio of both (industry) companies (ABC and DEF)?

  19. Thank you so much! 👏🏻👏🏻👏🏻 it’s really good lessons you are providing here without putting fees and that’s such a huge thing these days ☹️ many thanks 🙏🏻 even big professors can’t do what you’re doing. Really grateful ✨

  20. I'm watching this because of the negative interest rates floating around which after watching this video, I am more certain that our financial lenders have gone mad.

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