Deck 6: Real Interest Rates

Question 1

If the ex-post real interest rate is 5 percent and actual inflation rate is 2 percent, the nominal interest rate is

A)7 percent.
B)3 percent.
C)2.5 percent.
D)2 percent.

Answer 1

A

Question 2

What is the real present value of $5,202 to be received after two years if the expected rate of inflation over the next two years is 2 percent ?

A)​$5,000
B)$4,105
C)​$4,807
D)​$5,100

Answer 2

A

Question 3

If the expected inflation rate was 7 percent and the actual inflation rate was 3 percent, then

A)borrowers gained in real terms at the expense of lenders.
B)lenders gained in real terms at the expense of borrowers.
C)borrowers and lenders were not affected.
D)the government gained because it collected more in taxes.

Answer 3

B

Question 4

Suppose you bought an inflation-indexed security for $12,000 in January 2013 which pays an annual interest of 4 percent.If the value of the inflation index in January 2013 was 106 and its value in January 2014 was 105, what is the value of the inflation-adjusted principal?

A)$12,114.29
B)​$11,342.58
C)​$8,000.60
D)​$13,126.41

Question 5

Another name for the expected real interest rate is the

A)securitized real interest rate.
B)realized real interest rate.
C)ex-post real interest rate.
D)ex-ante real interest rate.

Question 6

For every dollar's worth of goods and services bought today, the amount of money it will take in N years to buy the same amount of goods and services when the average future inflation rate is p^eis called the______ .

A)realized inflation discount factor.
B)future inflation discount factor.
C)future-augmented inflation factor.
D)past-adjusted inflation factor.

Question 7

The nominal interest rate adjusted for actual inflation is the

A)expected real interest rate.
B)realized real interest rate.
C)after-tax real interest rate.
D)yield curve.

Question 8

For every dollar's worth of goods and services bought at an earlier date, the amount of money it would take now to buy the same amount of goods and services after N years of inflation at rate p is called the inflation______ discount factor.

A)future
B)realized
C)expected
D)past

Question 9

If the expected inflation rate is 4 percent, the nominal interest rate is 6 percent, and the actual inflation rate turns out to be 2 percent, then the realized real interest rate is _____than the expected real interest rate and borrowers______relative to lenders.

A)less; gain
B)less; lose
C)greater; gain
D)greater; lose

Question 10

If the expected inflation rate is 3 percent, the nominal interest rate is 5 percent, and the actual inflation rate turns out to be 4 percent, then the realized real interest rate is_____than the expected real interest rate and borrowers_____ relative to lenders.

A)less; gain
B)less; lose
C)greater; gain
D)greater; lose

Question 11

The real interest rate is the nominal interest rate adjusted for expected or actual

A)unemployment.
B)production.
C)income growth.
D)inflation.

Question 12

If the nominal interest rate was 4 percent, the expected real interest rate was 3 percent, and the realized real interest rate was 5 percent, then the expected inflation rate was ______and the realized inflation rate was_____ .

A)?1 percent; 1 percent
B)?1 percent; 2 percent
C)1 percent; ?1 percent
D)1 percent; 1 percent

Question 13

The amount of interest paid on a debt security in dollar terms as a percent of the principal is referred to as the

A)expected real interest rate.
B)realized real interest rate.
C)after-tax real interest rate.
D)nominal interest rate.

Question 14

The price of a certain amount of goods and services a year back was $200.If price increased by 4 percent during the year, how much money is required to buy the same amount of goods today?

A)$208
B)$204
C)$400
D)$404

Question 15

Another name for the realized real interest rate is the

A)securitized real interest rate.
B)expected real interest rate.
C)ex-post real interest rate.
D)ex-ante real interest rate.

Question 16

The nominal interest rate adjusted for expected inflation is the

A)expected real interest rate.
B)realized real interest rate.
C)after-tax real interest rate.
D)yield curve.

Question 17

From 1972 to 1974, the expected real interest rate on short-term bonds averaged about +2 percent, but the realized real interest rate averaged about −2 percent.The main reason for the difference was that

A)actual inflation was about 4 percentage points lower than expected inflation.
B)actual inflation was about 4 percentage points higher than expected inflation.
C)a monopoly cornered the market on short-term bonds.
D)nominal rate of interest was zero.

Question 18

If the expected inflation rate was 4 percent and the actual inflation rate was 6 percent, then

A)borrowers gained in real terms at the expense of lenders.
B)lenders gained in real terms at the expense of borrowers.
C)borrowers and lenders were not affected.
D)the government lost because it collected less in taxes.

Question 19

$\text { Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you } \$ 1,500 \text { in real (inflation- }$ adjusted) terms in one year.The nominal interest rate is 4 percent and the expected inflation rate is 2 percent.What is the present value of the bond? (Round off your answer to the nearest dollar and pick the answer closest to the one you calculate.)

A)$1,415
B)$1,442
C)$1,471
D)$1,530

Question 20

John bought an inflation-indexed security for $10,000 in January 2014.The security promises an annual interest rate of 5 percent and makes payments twice a year.If the value of the inflation index in January 2014 was 106 and its value in July 2014 was 105, John will receive an interest income of______ .

A)?$504.76
B)?$226.40
C)?$182.72
D)$368.56

Question 21

Investors can lock in a real interest rate and thus avoid most of the risk of unexpected inflation by buying

A)corporate bonds.
B)inflation-indexed securities.
C)stock.
D)mortgage-backed securities.

Question 22

According to the Fisher hypothesis, if the real interest rate is 2 percent and the inflation rate falls from 3 percent to 1 percent, then the nominal interest rate will_____percentage points and the real interest rate will decline by______ percentage points.

A)decline by 0; 2
B)increase by 2; 2
C)increase by 0; 0
D)decline by 2; 0 percentage points and the real interest rate will decline by

Question 23

If actual inflation was 4 percent over the past year and you owned a one-year bond that paid 6 percent interest, what was your after-tax realized real interest rate if your tax rate was 15 percent?

A)−0.6 percent
B)0.0 percent
C)1.1 percent
D)2.0 percent

Question 24

Which of the following happens when the expected inflation rate rises?​

A)​Both the demand and supply curve for bonds shift upward.
B)The demand curve for bonds shift to the left.
C)​The supply curve for bonds shift to the right.
D)​The expected real interest rate rises.

Question 25

Realized real interest rates in the United States were often negative in the early

A)1960s.
B)1970s.
C)1980s.
D)1990s.

Question 26

In recessions, the long-term expected real interest rate usually

A)rises.
B)declines.
C)stays unchanged.
D)rises early in the recession; declines later in the recession.

Question 27

If you expect inflation to be 2 percent next year and you buy a one-year bond paying 5 percent interest, what is your after-tax expected real interest income if the price of the bond is $200 and your tax rate is 40 percent?

A)$0.20
B)$20
C)$10
D)$2

Question 28

If you expect inflation to be 3 percent next year and you buy a one-year bond paying 4 percent interest, what is your after-tax expected real interest rate if you face a tax rate of 30 percent?

A)−0.2 percent
B)0.0 percent
C)0.3 percent
D)1.0 percent

Question 29

If the actual inflation was 4 percent over the past year and you owned a one-year bond that paid 4 percent interest, what was your after-tax realized real interest rate if your tax rate was 15 percent?

A)−0.6 percent
B)0.0 percent
C)1.1 percent
D)2.0 percent

Question 30

According to the Fisher hypothesis, if the real interest rate is 5 percent and the inflation rate rises from 2 percent to 4 percent, then the nominal interest rate will _____percentage points and the real interest rate will change by ______percentage points.

A)rise by 0; ?2
B)fall by 2; ?2
C)rise by 2; 0
D)fall by 1; 1

Question 31

$\text { Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you } \$ 1,500 \text { in real (inflation- }$ adjusted) terms each year for the next five years, plus your real principal of $75,000 at the end of the fifth year.The nominal interest rate is 5 percent and the expected inflation rate is 2 percent.What is the present value of the bond? (Round off your answer to the nearest thousand dollars and pick the answer closest to the one you calculate.)

A)$65,000
B)$68,000
C)$72,000
D)$75,000

Question 32

Which of the following will NOT play a role in eliminating the shortcoming of the taxation system, particularly the fact that the tax system taxes nominal return rather than real return?

A)Eliminating taxation of interest
B)Introducing inflation-indexed bonds
C)Taxing only real interest income, not nominal interest income
D)Reducing inflation to zero

Question 33

The hypothesis that an increase in the expected inflation rate will cause the nominal interest rate to rise and the real interest rate to remain unchanged is the

A)Fisher hypothesis.
B)rational-expectations theory.
C)Okun's hypothesis.
D)Keynesian hypothesis.

Question 34

Realized real interest rates in the United States were the highest in the

A)1960s.
B)1970s.
C)1980s.
D)1990s.

Question 35

Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you $1,500 in real (inflation- adjusted) terms in one year.The real interest rate is 3 percent.What is the present value of the bond? (Round off your answer to the nearest dollar and pick the answer closest to the one you calculate.)

A)$1,415
B)$1,456
C)$1,471
D)$1,530

Question 36

According to the Fisher hypothesis, an increase in the expected inflation rate should lead to____ in the nominal Interest rate and ____ in the expected real interest rate.

A)an increase; a decrease
B)an increase; no change
C)an increase; an increase
D)a decrease; a decrease

Question 37

One way that homeowners and banks can share the risk of inflation is through

A)fixed-rate mortgages.
B)refinancing.
C)default.
D)adjustable-rate mortgages.

Question 38

Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you $1,500 in real (inflation- adjusted) terms each year for the next five years, plus your real principal of $75,000 at the end of the fifth year.The nominal interest rate is 5 percent and the expected inflation rate is 3 percent.What is the present value of the bond? (Round off your answer to the nearest thousand dollars and pick the answer closest to the one you calculate.)

A)$65,000
B)$70,000
C)$74,000
D)$75,000

Question 39

One year ago, you bought a bond for $40,000.Today, you received the $40,000 principal back plus an interest of $2,000.If the inflation rate over the last year was 3 percent, calculate your real return (Round off your answer to the nearest percentage point).

A)2 percent
B)3 percent
C)4 percent
D)5 percent

Question 40

In recessions, the short-term expected real interest rate usually

A)rises by about 4 percentage points.
B)rises by about 2 percentage points.
C)declines by about 2 percentage points.
D)declines by about 4 percentage points.

Question 41

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the expected real interest rate is unchanged at 3.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate falls from 6 percent to 0 percent, the after-tax expected real interest rate

A)rises by 1.8 percent.
B)rises by 0.9 percent.
C)falls by 0.9 percent.
D)falls by 1.8 percent.

Question 42

How can the expected inflation rate be measured?

Question 43

If your after-tax realized real interest rate was 1 percent over the past year and you owned a one-year bond that paid 6 percent interest, what was the inflation rate if your tax rate was 15 percent?

A)3.95 percent
B)4.1 percent
C)4.25 percent
D)5.0 percent

Question 44

Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you $2,500 in real (inflation- adjusted) terms each year for the next five years, plus your real principal of $100,000 at the end of the fifth year.The nominal interest rate is 4 percent and the expected inflation rate is 1 percent.What is the present value of the bond? Show your work.

Question 45

Explain why inflation risk is a problem for investors.

Question 46

If your after-tax expected real interest rate is 3 percent on a one-year bond that pays 4 percent interest, what is the expected inflation rate if you face a tax rate of 20 percent?

A)0.0 percent
B)0.2 percent
C)2.0 percent
D)20.0 percent

Question 47

One year ago, you bought a bond for $10,000.You received interest of $400 at the end of the year, as well as your
$10,000 principal.If the inflation rate over the last year was 5 percent, calculate your real return.Show your work.

Question 48

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the after-tax expected real interest rate is unchanged at 2.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate falls from 6 percent to 0 percent, the nominal interest rate

A)rises by 8.5 percent.
B)rises by 4.25 percent.
C)falls by 4.25 percent.
D)falls by 8.5 percent.

Question 49

Describe how inflation interacts with the tax system to distort savings and thus affect investment.Is this problem more severe now or less severe than it has been in the prior 20 years? Why?

Question 50

Mary bought a bond ​a debt security for $2,500 with a nominal interest rate of 5 percent.If the inflation rate is 4 percent and Mary must pay 30 percent of her income in taxes, her after-tax nominal interest income is .

A)​$87.50
B)​$22.50
C)​$37.50
D)​$48.50

Question 51

The president of the United States is considering two different candidates to chair the Federal Reserve.If he chooses Alan, the probability that inflation will be 2 percent is 0.4 and the probability that inflation will be 4 percent is 0.6.If the president chooses Ben, the probability that inflation will be 2 percent is 0.6 and the probability that inflation will be 3 percent is 0.4.If you are an investor with your funds invested in bonds paying 7 percent, calculate the standard deviation of your real return if Alan is chosen to chair the Fed and if Ben is chosen to chair the Fed.Which candidate would you prefer? Explain why.

Question 52

If your after-tax expected real interest rate is 3 percent and your expected inflation rate is 2 percent, what was the nominal interest rate on your one-year bond if you faced a tax rate of 20 percent?

A)5.0 percent
B)5.75 percent
C)6.0 percent
D)6.25 percent

Question 53

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the expected real interest rate is unchanged at 3.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate rises from 3 percent to 6 percent, the after-tax expected real interest rate

A)rises by 1.8 percent.
B)rises by 0.9 percent.
C)falls by 0.9 percent.
D)falls by 1.8 percent.

Question 54

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the after-tax expected real interest rate is unchanged at 2.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate rises from 3 percent to 6 percent, the nominal interest rate

A)rises by 3 percent.
B)rises by 4.25 percent.
C)falls by 4.25 percent.
D)falls by 3 percent.

Question 55

If your after-tax realized real interest rate was 1 percent over the past year and the inflation rate was 3 percent, what was the nominal interest rate on your one-year bond if your tax rate was 15 percent?

A)4.45 percent
B)4.7 percent
C)5.0 percent
D)5.25 percent

Question 56

If your after-tax realized real interest rate was 2 percent over the past year and you owned a one-year bond that paid 8 percent interest, what was the inflation rate if you faced a tax rate of 15 percent?

A)4.8 percent
B)5.1 percent
C)5.4 percent
D)6.0 percent

Question 57

Answer the questions below.
a.Suppose the Fisher hypothesis holds for an economy that has an expected real interest rate of 3 percent.For each of the expected inflation rates of 0, 3, 6, 9, and 12 percent, calculate the after-tax expected real interest rate (expressed in percentage points with two decimals), if the tax rate is 15 percent.

b.Suppose the Fisher hypothesis does not hold, but instead that the after-tax expected real interest rate will be unchanged at 2.5 percent if the expected inflation rate changes.For each of the expected inflation rates of 0, 3, 6, 9, and 12 percent, calculate the (before-tax) expected real interest rate (expressed in percentage points with two decimals), if the tax rate is 15 percent.

Question 58

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the after-tax expected real interest rate is unchanged at 2.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate falls from 6 percent to 0 percent, the expected real interest rate

A)rises by 1.25 percent.
B)rises by 2.5 percent.
C)falls by 2.5 percent.
D)falls by 1.25 percent.

Question 59

Suppose that a change in the expected inflation rate leads supply and demand to adjust so that the after-tax expected real interest rate is unchanged at 2.0 percent.The tax rate is 30 percent.Initially, the expected inflation rate is 3.0 percent.If the expected inflation rate rises from 3 percent to 6 percent, the expected real interest rate

A)rises by 0.75 percent.
B)rises by 1.25 percent.
C)falls by 1.25 percent.
D)falls by 0.75 percent.