The Economics of Money, Banking, and Financial Markets

Frederic S. Mishkin

Chapter 4

Understanding Interest Rates - all with Video Answers

Educators

Chapter Questions

Problem 1

Would a dollar tomorrow be worth more to you today when the interest rate is $20 \%$, or when it is $10 \% ?$

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 2

Write down the formula that is used to calculate the yield to maturity on a twenty-year $10 \%$ coupon bond with $\$ 1,000$ face value that sells for $\$ 2,000$.

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 3

To pay for college, you have just taken out a $\$ 1,000$ government loan that makes you pay $\$ 126$ per year for 25 years. However, you dont have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than $12 \%$ (this is the yield to maturity on a normal $\$ 1,000$ fixed-payment loan in which you pay $\$ 126$ per year for $25 \text { years }) ?$

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 4

Is it better for bondholders when the yield to maturity increases or decreases?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 5

A financial adviser has just given you the following advice: "Long-term bonds are a great investment because their interest rate is over $20 \%$. " Is the financial adviser necessarily right?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 6

If mortgage rates rise from $5 \%$ to $10 \%$ but the expected rate of increase in housing prices rises from $2 \%$ to $9 \%$ are people more or less likely to buy houses?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 7

When is the current yield a good approximation to the yield to maturity?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 8

Why would a government choose to issue a perpetuity. which requires payments forever, instead of a terminal loan, such as a fixed-payment loan, discount bond, or coupon bond?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 9

Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 10

True or False: With a discount bond, the return on a bond is equal to the rate of capital gain.

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 11

If interest rates decline, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 12

Interest rates were lower in the mid- 1980 s than in the late 1970 s, yet many economists have commented that real interest rates were actually much higher in the mid$1980 s$ than in the late 1970 s. Does this make sense? Do you think that these economists are right?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 13

Retired persons often have much of their wealth placed in savings accounts and other interest-bearing investments, and complain whenever interest rates are low. Do they have a valid complaint?

Kaylee Mcclellan

Kaylee Mcclellan

Numerade Educator

Problem 14

If the interest rate is $10 \%$, what is the present value of a security that pays you $\$ 1,100$ next year, $\$ 1,210$ the year after, and $\$ 1,331$ the year after that?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 15

Calculate the present value of a $\$ 1,000$ discount bond with five years to maturity if the yield to maturity is $6 \%$

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 16

A lottery claims its grand prize is $\$ 10$ million, payable over 5 years at $\$ 2,000,000$ per year, If the first payment is made immediately, what is this grand prize really worth? Use an interest rate of $6 \%$

Anand Jangid

Numerade Educator

Problem 17

What is the yield to maturity on a $\$ 1,000$ -face-value discount bond maturing in one year that sells for $\$ 800 ?$

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 18

What is the yield to maturity on a simple loan for S1 million that requires a repayment of $\$ 2$ million in five years' time?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 19

Which $\$ 1,000$ bond has the higher yicld to maturity, a twenty-year bond selling for $\$ 800$ with a current yield of $15 \%$ or a one-year bond selling for $\$ 800$ with a current yield of $5 \% ?$

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 20

Consider a bond with a $4 \%$ annual coupon and a face value of $\$ 1,000 .$ Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?
$$\begin{array}{|ccc|}
\hline \text { Years to } & \text { Yield to } & \text { Current } \\
\text { Maturity } & \text { Maturity } & \text { Price } \\
\hline 2 & 2 \% & \\
2 & 4 \% & \\
3 & 4 \% & \\
5 & 2 \% & \\
5 & 6 \% & \\
\hline
\end{array}$$

John Lee

Numerade Educator

Problem 21

Consider a coupon bond that has a $\$ 1,000$ par value and a coupon rate of $10 \%$. The bond is currently selling for $\$ 1,044.89$ and has two years to maturity. What is the bond's yield to maturity?

Andrew Davis

Numerade Educator

Problem 22

What is the price of a perpetuity that has a coupon of $\$ 50$ per year and a yield to maturity of $2.5 \% ?$ If the yield to maturity doubles, what will happen to its price?

Sanchit Jain

Numerade Educator

Problem 23

Property taxes in a particular district are $4 \%$ of the purchase price every year. If you just purchased a $\$ 250,000$ home, what is the present value of all the future property tax payments? Assume that the house remains worth $\$ 250,000$ forever, property tax rates never change, and that a $6 \%$ interest rate is used for discounting.

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 24

A $\$ 1000$ -face-value bond has a $10 \%$ coupon rate, its current price is $5960,$ and it is expected to increase to $\$ 980$ next year. Calculate the current yield, the expected rate of capital gain, and the expected rate of return.

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 25

Assume you just deposited $\$ 1,000$ into a bank account. The current real interest rate is $2 \%$, and inflation is expected to be $6 \%$ over the next year. What nominal rate would you require from the bank over the next year? How much money will you have at the end of one year? If you are saving to buy a fancy bicycle that currently sells for $\$ 1,050,$ will you have enough to buy it?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator