The Profs| Professional University Tutors London| Our higher education specialists created this to clarify a commonly misunderstood but important university topic - The Difference Between Nominal & Real Interest Rates. http://theprofs.co.uk/resources/nominal-real-interest-rates-the-fischer-equation-approximation/ See how Sally the Squirrel gets left hoping by banks because she doesn't understand how interest rates work, and this has huge real-life ramifications for mortgage-owners. You have been warned!

1.
F ir s t - C la s s U n iv e r s it y T u t o r s
Interest
Rates,
Inflation
and
the
Fisher
Equation
Inflation
is
an
increase
in
the
general
price
level.
Expected
inflation
rate
is
𝑃! − 𝑃!
𝑖 =
𝑃!
Quick
Maths
If
the
current
price
level
is
£1,
meaning
that
the
average
good
costs
£1,
and
£".!"!£"
the
expected
price
level
is
£1.10
next
year
the
inflation
is
£" = 10%
The
Nominal
Interest
Rate,
R
is
in
terms
of
money
and
includes
inflation.
If
you
save
£1
today
then
you
will
receive
£(1+R)
pounds
tomorrow.
Economists
often
say
that
the
Real
Interest
Rate,
r
is
in
terms
of
goods
-­‐
if
you
save
one
unit
of
goods
today
then
you
will
receive
(1
+
r)
units
of
goods
tomorrow
–
which
is
very
unclear
as
banks
don’t
tend
to
let
you
put
you
car
into
a
vault
and
return
it
with
an
extra
steering
wheel
as
interest.
Nominal
Interest
Rates
vs.
Real
Interest
Rates
The
real
interest
rate
accounts
for
inflation
whereas
the
nominal
interest
rate
does
not.
Here’s
an
example
to
illustrate
the
difference:
Lets
clear
this
up:
Sally
the
Squirrel
has
£100
to
save
for
next
year’s
cold
winter.
A
nut
costs
£4
today
so
she
could
have
purchased
25
nuts
this
year
and
buried
them
away.
But
like
many
squirrels
she
is
somewhat
forgetful.
Instead
she
goes
to
her
bank
-­‐
NutWest
-­‐
and
they
offer
her
a
savings
account
with
40%
interest
(R
=
40%).
Banks
always
offer
rates
in
nominal
terms
as
they
don’t
understand
economics.
Plus
this
way
they
get
to
rob
poor
squirrels
blind.
Poor
Sally
saves
her
£100
thinking
she’s
going
to
receive
enough
interest
to
buy
an
extra
10
nuts
next
year,
which
would
be
40%
more
nuts.
Poor
Sally
should
have
studied
economics.
Due
to
many
squirrels
unable
to
find
their
buried
nuts
the
price
of
nuts
rises
greatly
over
the
year.
As
nuts
are
the
only
good
in
the
squirrel
economy,
this
is
inflation,
and
the
price
rises
a
whooping
25%
so
that
now
nuts
cost
£5!
When
Sally
goes
back
to
the
bank
she
receives
her
£100
plus
£40
interest
–
a
40%
return
on
her
money.
However,
when
she
goes
to
spend
this
£140
she
finds
that
it
only
buys
her
28
nuts
at
the
new
price
of
£5
per
nuts.
She
feels
robbed.
The
40%
interest
rate
was
nominal
because
it
did
not
account
for
inflation.
In
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2.
F ir s t - C la s s U n iv e r s it y T u t o r s
terms
of
goods
(as
economists
would
say),
she
was
not
able
to
buy
10
more
nuts,
but
only
3
more
nuts.
So
the
real
interest
rate,
telling
us
what
our
money
can
really
afford
in
terms
of
goods,
and
which
accounts
for
inflation,
was
lower.
In
this
example,
she
could
previous
afford
25
nuts,
now
she
can
afford
28
so
28 ÷ 25 = 1.12
(r=12%)
In
the
real
world,
where
inflation
and
interest
rates
are
much
smaller
than
the
above
example,
then
an
accurate
approximate
for
the
Fisher
Equation
,
which
describes
the
relationship
between
the
real,
nominal
and
inflation
rates
is.
𝑅 = 𝑟 + 𝑖
If
inflation
is
positive,
which
it
generally
is,
then
the
real
interest
rate
is
lower
than
the
nominal
interest
rate.
If
we
have
deflation,
meaning
that
the
inflation
rate
is
negative,
then
the
real
interest
rate
will
be
larger.
For
an
exact
mathematical
relationship,
read
on:
The
real
interest
rate
is
the
interest
from
savings
in
terms
of
goods
rather
than
money.
We
must
convert
goods
into
money,
invest
the
money
and
then
convert
back
into
goods
at
the
new
prices.
Ø One
unit
of
goods
buys
P
units
of
today’s
money
Ø Saving
P
units
of
unit
today
returns
you
𝑃! (1 + 𝑅)
units
of
tomorrow’s
money.
!
Ø 𝑃! (1 + 𝑅)
units
of
tomorrow’s
money
will
buy
you
!
goods
tomorrow
!
Therefore
1+ 𝑟 =
𝑃! × (1 + 𝑅)
𝑃!
1+ 𝑟 =
(1 + 𝑅)
𝑃!
𝑃!
1+ 𝑟 =
(1 + 𝑅)
(1 + 𝑖)
or
(1 + 𝑟)(1 + 𝑖) = (1 + 𝑅)
Note:
the
approximation
works
because
𝑟 𝑖
is
negligible
because
both
r
and
i
are
such
small
numbers
and
then
the
1s
cancel
out.
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