Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

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Answer 1

Textbook Question

Chapter 3, Problem 35PS

Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

Chapter 3, Problem 35PS, Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds?

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

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Answer 2

Textbook Question

Chapter 3, Problem 35PS

Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

Chapter 3, Problem 35PS, Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds?

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

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Answer 3

Textbook Question

Chapter 3, Problem 35PS

Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

Chapter 3, Problem 35PS, Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds?

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

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Answer 4

Textbook Question

Chapter 3, Problem 35PS

Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds? Assume for simplicity that the bonds pay annual coupons. The price of a one-year strip is 97.56%, and the price of a four-year strip is 87.48%.

Chapter 3, Problem 35PS, Prices and spot interest rates What spot interest rates are implied by the following Treasury bonds?

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

Answer 8

Expert Solution & Answer

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)

Solve equation 1 and 2

$1,005.419512–(2.5×$37.030021)=$1,050−(2.5×$20)(1+r3)3=$912.844459$1,000(1 +r3)3r3=0.030863, or 3.0863%

Determiner2:

r2 can be solved by 3-year bond and r3 and r1

$1,054.20=$501.025+$50(1+r2)2+$1,0501.0308633$46.932036=$50(1+r2)2=0.0322

Hence, the spot rates are 2.50%, 3.22%, 3.09%, 3.40% and 3.60 for years 1 to 5.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Summary Introduction

To determine: The spot interest rates implied by treasury bonds.

Answer 12

Explanation of Solution

Determine r1:

$97.56=$100(1+r1)(1+r1)=$100$97.56=2.50%

Hence, r1 is 2.50%.

Determiner4:

$87.48=$100(1+r4)(1+r4)=$100$87.48=3.40%

Hence, r1 is 3.40%.

Determiner5:

r5 can be solved by eliminating the 1-4 cash flow of 1.5 times 2% coupon bond and 3% coupon bond.

(1.5×$928.90)–$974.30=[1.5×$1,020–($1,030)](1+r5)5=0.036 or 3.6%

Determiner3:

r3 can be solved by reducing the 3-year, 5% coupon bond and 2.5 times of reduced 5-year 2% coupon bond which eliminates the 2-year cash flow:

$928.90=$201.025+$20(1+r2)2+$20(1+r3)3+$201.0344+$1,0201.0359555.....(1)$1,054.20=$501.025+$50(1+r2)2+$1,050(1+r3)3 $1,005.419512=$50(1+r2)2+$1,050(1+r3)...........(2)