9/25/2020
Aplia:
Student
Question
<
Back
to
Assignment
Attempts:

0.3



Keep
the
Highest:
0.3/
2
8.
Inflationinduced
tax
distortions
Charles
receives
a
portion
of
his
income
from
his
holdings
of
interestbearing
U.S.
government
bonds.
The
bonds
offer
a
real
interest
rate
of
4.5%
per
year.
The
nominal
interest
rate
on
the
bonds
adjusts
automatically
to
account
for
the
inflation
rate.
The
government
taxes
nominal
interest
income
at
a
rate
of
10%.
The
following
table
shows
two
scenarios:
a
lowinflation
scenario
and
a
high
inflation
scenario.
Given
the
real
interest
rate
of
4.5%
per
year,
find
the
nominal
interest
rate
on
Charles's
bonds,
the
aftertax
nominal
interest
rate,
and
the
aftertax
real
interest
rate
under
each
inflation
scenario.
Inflation
Rate
Real
Interest
Rate
Nominal
Interest
Rate
AfterTax
Nominal
Interest
Rate
(Percent)
(Percent)
(Percen
(Percen
@J
[5.85]
AfterTax
Real
Interest
Rate
(Percen3
g5
2.0
4.5

25

225
12_6\
9.5
4.5

45
[X
Explanation:

4.05
31

405
[X
Points:
0/1
Close
Explanation
To
maintain
the
level
of
the
real
interest
rate,
the
nominal
interest
rate
must
adjust
according
to
the
Fisher
equation:
Nominal
Interest
Rate
=
Real
Interest
Rate
+
In
flation
At
the
lower
inflation
rate
of
2%
per
year,
the
nominal
interest
rate
is
6.5%,
the
4.5%
real
rate
plus the
2%
inflation
rate.
At
the
higher
inflation
rate
of
9.5%
per
year, the
nominal
interest
rate
is
14%,
the
4.5%
real
rate
plus
the
9.5%
inflation
rate.
The
government
taxes
10%
of
the
nominal
interest
paid
on
the
bonds.
When
the inflation
rate
is
2%
per
year
and
the
nominal
interest
rate
is
6.5%
per
year,
the
tax
reduces
the
nominal
interest
payment
from
6.5%
to
an
aftertax
nominal
interest
payment
of
6.5%
—
(0.1
x
6.5%)
=
5.85%
per
year.
At
an
inflation
rate
of
9.5%
per
year
and
a
nominal
interest
rate
of
14%
per
year,
the
tax
reduces
the
nominal
interest
payment
from
14%
to
an
aftertax
nominal
interest
payment
of
14%
—
(0.1
x
14%)
=
12.6%
per
year.
Rearranging
the
nominal
interest
rate
equation,
you
can
see
that
the
real
interest
rate
is
the
difference
between
the
nominal
interest
rate
and
the
inflation
rate.
The
aftertax
real
interest
rate
is,
therefore,
the
aftertax
nominal
interest
rate
minus
the
inflation
rate.
At
the
lower
inflation
rate,
the
aftertax
real
interest
rate
is
calculated
as
follows:
AfterTax
Real
Interest
Rate
AfterTax
Nominal
Interest
Rate
—
Inflation
Rate
5.85%
—
2%
3.85%
At
the
higher
inflation
rate,
the
aftertax
real
interest
rate
is
12.6%
—
9.5%
=
3.1%,
which
is
lower
than
the
aftertax
real
return
at
the
lower
inflation
rate.
https://ng.cengage.com/static/nb/ui/evo/index.html?deploymentld=5982802231695134071648923390&elSBN=9780357133637&id=865181431&snap...
1/2