Question 1

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 2-year zero coupon bond be if it is purchased today and has face value of $1,000?

Accepted Answer

The answer of \[\begin{array} { l | l } 
\hline...

Question 2

Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face value $1,000 and 5 years to maturity.

Accepted Answer

The price of the bond can be calculated using the following formula:

Price = (C / r) x [1 - 1 / (1 + r)^n] + F / (1 + r)^n

where C is the annual coupon payment, r is the discount rate, n is the number of periods, and F is the face value.

Plugging in the values, we get:

Price = (80 / 0.08) x [1 - 1 / (1 + 0.08)^5] + 1000 / (1 + 0.08)^5
Price = $1,084.25

Therefore, the best choice is C.

Question 3

What would the yield to maturity be on a four-year zero coupon bond purchased today?

Accepted Answer

The correct answer is A because the yield to maturity on a zero coupon bond is equal to the annual rate of return, which is 5.75%.

Question 4

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 1-year zero coupon bond be if it is purchased today and has face value of $1,000?

Accepted Answer

The answer of \[\begin{array} { l | l } 
\hline...

Question 5

Given the yield on a 3 year zero-coupon bond is 7% and forward rates of 6% in year 1 and 6.5% in year 2,what must be the forward rate in year 3?

Accepted Answer

To solve the problem, we can use the formula of calculating forward rate:

(1+ f3)^3 = (1+ r3) * (1+ f1)^1 * (1+ f2)^2

where f1 and f2 are the given forward rates, and r3 is the unknown forward rate in year 3.

Plugging in the values, we get:

(1+ r3)^3 = (1+ 7%) * (1+ 6%) * (1+ 6.5%)
(1+ r3)^3 = 1.07 * 1.06 * 1.065
(1+ r3)^3 = 1.2034

Taking cube root on both sides, we get:

1 + r3 = 1.085
r3 = 0.085 = 8.5%

Therefore, the answer is (C) 8.5%.

Question 6

What is the yield to maturity on a 3-year zero coupon bond?

Accepted Answer

The answer of What is the yield to maturity on...

Question 7

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 5-year zero coupon bond be if it is purchased today and has face value of $1,000?

Accepted Answer

Using the formula for calculating present value of a zero coupon bond, we have:

$$P_0 = \frac{FV}{(1 + r)^t}$$

where $P_0$ is the purchase price of the bond, $FV$ is the face value of the bond, $r$ is the annual interest rate, and $t$ is the time to maturity in years.

For the given bond, $FV = 1,000$ and $t = 5$. To find the appropriate interest rate, we need to use the 5-year forward rate, which is the interest rate for a loan that starts five years from now. Based on the given information, we know that the 5-year forward rate is 5.8%.

Plugging values into the formula, we get:

$$P_0 = \frac{1,000}{(1 + 0.058)^5} = 776.14$$

Therefore, the purchase price of the bond should be $776.14. The answer is A.

Question 8

What is the yield to maturity of a 5-year bond?

Accepted Answer

The answer of What is the yield to maturity of...

Question 9

You have purchased a 4-year maturity bond with a 9% coupon rate paid annually.The bond has a par value of $1,000.What would the price of the bond be one year from now if the implied forward rates stay the same?

Accepted Answer

The correct answer is A because the price of the bond one year from now will be $995.63. This is because the bond has a 9% coupon rate, which means that the bondholder will receive $90 in interest payments each year. The bond also has a par value of $1,000, which means that the bondholder will receive $1,000 when the bond matures in four years. The price of the bond one year from now will be the present value of the future cash flows, which is $995.63.

Question 10

What is the yield to maturity of a 3-year zero coupon bond?

Accepted Answer

The answer of What is the yield to maturity of...

Question 11

What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)

Accepted Answer

We can use the Bond Pricing Formula to find the price of the bond:
Price = (Coupon payment / (1 + i)^1) + (Coupon payment / (1 + i)^2) + (Coupon payment / (1 + i)^3) + (Coupon payment + Par value / (1 + i)^4)
Where:
Coupon payment = $1000 x 10% = $100
Par value = $1000
i = Yield to maturity
n = 4 (number of years until maturity)

Since the coupon rate is the same as the yield to maturity, we know that the bond is being sold at par. Therefore, yield to maturity = Coupon rate = 10%

Price = ($100 / 1.10^1) + ($100 / 1.10^2) + ($100 / 1.10^3) + ($1000 / 1.10^4) = $1,035.66

Therefore, the answer is C.

Question 12

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 3-year zero coupon bond be if it is purchased today and has face value of $1,000?

Accepted Answer

The answer of \[\begin{array} { l | l } 
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Question 13

What is the yield to maturity of a 4-year bond?

Accepted Answer

The yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. The correct YTM is calculated based on the bond's current market price, coupon interest rate, and time to maturity. In this case, the correct YTM is 5.02%.

Question 14

If you have just purchased a 4-year zero coupon bond,what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)

Accepted Answer

A zero coupon bond does not make any periodic interest payments, instead it is issued at a discount to its face value and the investor receives the full face value at maturity. The return on investment in a zero coupon bond is the difference between the purchase price and the face value.

Given that the bond has a maturity of 4 years and is a zero coupon bond, we can use the implied forward rates for the corresponding periods to calculate the expected rate of return.

Assuming the implied forward rates do not change, the 1-year implied forward rate for a 3-year zero coupon bond is 3%. Therefore, the expected rate of return for the first year on the 4-year zero coupon bond would also be 3%.

Hence, the correct answer is B)3%.

Question 15

$$\begin{array} { | l | l | } 
\hline \text { Par Value } & \$ 1,000 \
\hline \text { Time to Maturity } & 18 \text { years } \
\hline \text { Coupon } & 9 ^ { \circ } \% ( \text { paid annually) } \
\hline \text { Current Price } & \$ 917.99 \
\hline \text { Yield to Maturity } & 10 ^ { \circ } \% \
\hline
\end{array}$$
-Given the bond described above,if interest were paid semi-annually (rather than annually),and the bond continued to be priced at $917.99,the resulting effective annual yield to maturity would be:

Accepted Answer

When interest is paid semi-annually, we need to adjust the coupon rate and the number of periods to maturity accordingly. The coupon rate becomes 4.5% (9%/2) per half-year, and there are now 36 (18*2) half-year periods to maturity.

Using the bond pricing formula with semi-annual periods:

$917.99 = \frac{45}{1+(r/2)^1} + \frac{45}{1+(r/2)^2} + ... + \frac{45+1000}{1+(r/2)^{36}}$

where r is the semi-annual yield to maturity.

We can solve for r using a financial calculator or Excel:

r = 5.25% (semi-annual)

To convert this semi-annual yield to an effective annual yield, we can use the following formula:

Effective annual yield = (1 + semi-annual yield)^2 - 1

Plugging in the semi-annual yield we just calculated:

Effective annual yield = (1 + 0.0525)^2 - 1 = 10.81%

Therefore, the resulting effective annual yield to maturity would be more than 10%.

Question 16

The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. $$\begin{array} { | l | l | } 
\hline \text { Maturity (Years) } & { \text { Price } } \
\hline 1 & \$ 925.16 \
\hline 2 & \$ 862.57 \
\hline 3 & \$ 788.66 \
\hline 4 & \$ 711.00 \
\hline
\end{array}$$
-What is,according to the expectations theory,the expected forward rate in the third year?

Accepted Answer

The expected forward rate for the third year can be calculated using the formula: $(1 + f_{3})^3 = \frac{(1 + y_3)^3}{(1 + y_2)^2}$, where $y_n$ is the yield for n years. Calculate $y_2$ and $y_3$ using the bond prices, then solve for $f_3$.

Question 17

What is the price of a 2-year maturity bond with a 5% coupon rate paid annually? (Par value = $1,000)

Accepted Answer

The answer of What is the price of a 2-year...

Question 18

What is the yield to maturity of a 1-year bond?

Accepted Answer

The yield to maturity of a 1-year bond is the annual rate of return an investor can expect to receive if they hold the bond until maturity. In this case, the yield to maturity is 4.6%.

Question 19

$$\begin{array} { l | l } 
\underline { Y e a r } & \underline { 1 - Y e a r } \text { Forward Rate } \
\hline 1 & 5 \% \
\hline 2 & 5.5 \% \
\hline 3 & 6.0 \% \
\hline 4 & 6.5 \% \
\hline 5 & 7.0 \% \
\hline
\end{array}$$
-What should the purchase price of a 2-year zero coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?

Accepted Answer

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Question 20

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 4-year zero coupon bond be if it is purchased today and has face value of $1,000?

Accepted Answer

The answer of \[\begin{array} { l | l } 
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Quiz 15: The Term Structure of Interest Rates

Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face value $1,000 and 5 years to maturity.

What would the yield to maturity be on a four-year zero coupon bond purchased today?

Given the yield on a 3 year zero-coupon bond is 7% and forward rates of 6% in year 1 and 6.5% in year 2,what must be the forward rate in year 3?

What is the yield to maturity on a 3-year zero coupon bond?

What is the yield to maturity of a 5-year bond?

You have purchased a 4-year maturity bond with a 9% coupon rate paid annually.The bond has a par value of $1,000.What would the price of the bond be one year from now if the implied forward rates stay the same?

What is the yield to maturity of a 3-year zero coupon bond?

What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)

What is the yield to maturity of a 4-year bond?

If you have just purchased a 4-year zero coupon bond,what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)

What is the price of a 2-year maturity bond with a 5% coupon rate paid annually? (Par value = $1,000)

What is the yield to maturity of a 1-year bond?