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## AP®︎/College Macroeconomics

### Course: AP®︎/College Macroeconomics > Unit 4

Lesson 1: Financial assets# Introduction to interest

AP.MACRO:

MEA (BI)

, MEA‑3 (EU)

, MEA‑3.A (LO)

, MEA‑3.A.2 (EK)

, MEA‑3.A.4 (EK)

Simple interest is calculated as a percentage of the original amount borrowed (the principal) and remains the same over time. Compound interest, on the other hand, takes into account the accumulated interest as well, meaning that the amount owed grows at a faster rate and the total sum owed will be higher than with simple interest. Created by Sal Khan.

## Want to join the conversation?

- Sal, you start this video saying, "well now that you've learned one of the most useful concepts in life...." Is that from a previous video? If so, which one? This appears to be the first in the sequence. If there is one that precedes this video, can you please add an back arrow, or let me know which video that is. Thank you! You guys are great. I've learned so much from you and your team.(58 votes)
- Yeah the compound interest one is before do that first(10 votes)

- Isn't it a bit illogical to charge 10% of 121 as interest after two years, and more as time passes? I mean, you still only have the original 100, but you are paying interest for a much higher amount. You'd be much cheaper off if you paid back after each year and then simply lent 100 bucks again immediately. That way, the distribution of the money would stay the same (bank minus a hundred, you a hundred richer) and you'd only pay interest for what you actually borrowed.

How do banks justify compound loans? I mean, whether the loan has been going on for decades or just a year, the "hole" in the bank's amount of money stays the same. What difference does it make if one guy borrows some money for a really long time as compared to ten people borrowing and returning the same amount subsqeuent to each other every year? Wouldn't the scenario with many borrowers actually be worse for the bank due to the increased risk of someone not being able to pay back? Why charge the single guy more??

I feel there's something I'm missing here.(35 votes)- Risk is part of it, but the "risk" of a loan is normally taken into account in the interest rate (higher risk = higher interest rate, regardless of the length of the loan). Another way to think of it is that interest is "due" every year even if you don't actually pay it. If you borrow money and do not pay the interest in a year, you are essentially now borrowing the interest payment itself on top of the principal you still have. Your loan (the principal) just got bigger by the interest payment you did not make. This sort of thing happens in practice. I have gotten loans and the fees I paid for the loan, the cost of processing the loan, and even the first year's interest payment were rolled into the loan itself, so that I paid nothing out of pocket. That way I was able to borrow the money I actually need to use for an investment but did not make any payments on what I borrowed for two years. For some investments - like construction or land development - it takes so long to be able to pay the loan back, or even make interest payments, that this is the only way to go.(20 votes)

- y is everything blurry i can't understand?(9 votes)
- Hey Uddip!

This video was made a while ago and the software wasn't quite what it is now. That might be why you're seeing it as a bit blurry. Most other videos are updated though so you shouldn't find this as too much of an issue in the rest of the course.

Hope this helps!(12 votes)

- Lets say that I lend out a Chemistry Textbook to someone and I say," You owe me $300 when you return this to me next year and there is a 20% interest rate per year that you have to use the book." (Do I need to specify if it is compound or simple or can the other person assume one or the other?) If you can answer my question can you give me the reasoning behind your answer as well?(9 votes)
- usually when you loan something you charge normal interest ,alternatively if you charge compound interest yes you will be getting more out of it but if the person was wise he wouldn't borrow it from you in the first place (but normally people charge simple interest and if they ask then you say simple interest)(11 votes)

- basically, after you borrow money, the more you wait the more you will owe money. is that an accurate statement?(5 votes)
- of course, just like the longer you rent a house the more you will pay in rent.(6 votes)

- At5:53Sal says, "But when you think about it, you're actually paying a smaller and smaller percentage of what you owe going into that year." He is referring to simple interest. I do not understand how you are paying a smaller percentage, when, by definition, you are paying the same amount every year.(3 votes)
- In my opinion I think...

The truth is you're actually paying a smaller and smaller percentage of interest if you don't using compound interest formula.

For example:

- I borrow you $100 with r(interest) = 10%, after one year - if I pay you back, I will have to pay you $110 ( This is okey )

- But what's happen when I don't pay you back, then in this case I owned you $110 and in the end of year two If you just compound $10 then I have to pay $120. The interest rate will no be 10% in the year two anymore ^^ 10/110 = 9.09 %

and in year 3 will be : $10 / 120 = 8.3 %

year 4 will be : 10/130= 7.69 %

^^(3 votes)

- Can you remake this video? the quality on it makes the numbers and words practically unreadable.(5 votes)
- From4:25to5:45, you are multiplying 100 and 10% each time, correct?(4 votes)
- you are not so much as multiplying as converting it to a fraction then to a percentage (or 10/100 to 10%)(2 votes)

- 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.(3 votes)
- Why do we multiply the 100% by 110 for compound interest?(2 votes)
- It is not a great explanation.

It goes like this... in 2 steps

$100 x 10% = $10

$100 + $10 = $110

$110 x 10% = $11

$100 + $11 = $121

The 100% in Sal's explanation refers to the principal.

The 10% refers to the interest.

Together it is 110%. So...

$100 x 110% = $110 (balance)

$110 x 110% = $121 balance... and so on.

To simply multiply the principal by 110% allows it to be calculated in 1 step, instead of my 2 steps above.(3 votes)

## Video transcript

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.