in this video we're going to talk about
how to calculate the yield of maturity
on a zero coupon bond so the yield of
maturity is the rate of return that you
would get if you purchased a bond at its
current price and then held the bond to
maturity so for example and now we're
course talking about zero coupon bonds
in this example let's say that you
bought a bond for ninety five thousand
two hundred and thirty-eight dollars in
the face value of the bond was a hundred
thousand so because it's a zero coupon
bond that we're talking about there's
not going to be any periodic interest
payments or anything like that it's just
a simple 1-year bond where you say okay
today I pay ninety five thousand two
thirty-eight in a year from now I get a
hundred thousand returned to me so that
difference between the hundred thousand
and the ninety five thousand two thirty
eight you could just think of that as
the interest that you've that you've
earned on that investment right so now
we want to say okay well what rate of
return is that right if you buy it for
this price and you get this a year later
what was your rate of return on that
investment so we can just go ahead and
calculate it out we can just use some
really simple algebra for example if we
took say our ninety five thousand two
hundred and thirty eight that we paid
this our price right and if we multiply
that by one plus the yield to maturity
that rate of return one plus the rate of
return times what we've invested think
of the price as our investment and
that's supposed to equal a hundred
thousand dollars right in terms of what
we've just set up here right that should
equal a hundred thousand dollars and
that'll yield or well give us our yield
to maturity all right so this is
basically saying look we take the
investment we multiply it by one plus
the rate of return and that's going to
give us what we get which is a hundred
thousand so we're trying to solve for
the yield so now you can go ahead and
just divide a hundred thousand by ninety
five thousand two thirty-eight right so
we're just dividing each side we're just
doing simple math here and so that'll
give us one
us the yield to maturity is going to be
equal to one point zero five now I've
done some rounding here so if it's not
exactly precise forgive me but we
basically just divided each side by
ninety five thousand two thirty-eight
and so now we've got this one plus the
yield is 1.05 and so we just subtract
one from each side and now we have our
yield is going to be 0.05 or we can just
think of that as a percentage we can
think of that as is 5% so what does this
mean this means that the rate of return
if we were to buy a bond today for
ninety five thousand two hundred and
thirty eight dollars it didn't have any
periodic interest payments anything like
that it's just a one-year bond so a year
from now we get a hundred thousand
dollars back we earned a rate of return
of five percent that's all that's saying
so now you might ask well what okay this
is a simple example we just got one year
here but what if we had multiple periods
what if we had a zero coupon bond that
was like two years three years four
years five how do we go about
calculating it so we've got a really
nice formula and I'll just show it to
you let's just say that we had a three
year bun let's say that we have the same
things as as above or it's a hundred
thousand dollar face value we're going
to pay ninety five thousand two thirty
eight but this time we're not going to
get that hundred thousand dollar face
value until three years later it's a
three year bond instead of a one year
bond so now I just want to show you this
formula will give us the result and give
us our yield every time and no matter
how many periods they are so we have n n
is going to be three and it's just a
number of periods right so I've got C
this n here that's the number of periods
and then FV that's the face value that's
going to be the hundred thousand let me
let me actually just start plugging in
some of these numbers here and I'll I'll
change up colors and make it a little
interesting
so our yield to maturity it's going to
be equal to and then this will be in
parentheses will have the face value of
one hundred thousand and then that's
going to be divided by the price ninety
five
238 and then we're going to take that
and raise it to a power write all this
in here in the parenthesis we're going
to raise to a power we're going to raise
it to the 1 over N power which is in
this case 3 and so we're just going to
raise it to the 1/3 power and then we're
going to after we've after we've got
this whole thing here we've calculated
that we're going to subtract out 1 so
let's scroll down so what are we going
to end up with here I'll just I'll just
go ahead and skip right to the chase
we're going to end up with point zero
one six right so if we're going to and
we can think about that in terms of a
percentage one point six percent so when
you put that into your calculator if it
doesn't come out exactly like this I
apologize I just did a little bit of
rounding but bottom line is that we just
use our formula here we've got n is the
number of periods so this let's say this
was a seven-year zero coupon bond then
we would raise this thing here to the
one seventh power right so that's where
the end comes in and then we just have
the face value of the bond in our case
it was a hundred thousand the price of
the bond right and so you just plug in
those numbers and it just very simply
gives you the yield to maturity which
we've been also we're just referring to
as the yield and so the yield of this
three-year zero coupon bond is going to
be one point six