Big House Nursery Inc. has issued 20 - year face value, annual coupon bonds, with a yield to
maturity of . The current price of the bond is
A.
B.
C.
D. There is not enough information to answer this question.

Ask by Mejia Hodgson. in the United States

Jan 24,2025

Question

Big House Nursery Inc. has issued 20 - year face value, annual coupon bonds, with a yield to
maturity of . The current price of the bond is
A.
B.
C.
D. There is not enough information to answer this question.

Ask by Mejia Hodgson. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To find the current price of the bond, we can use the formula for the price of a bond:

$$ P = \frac{C}{r} \times (1 - \frac{1}{(1 + r)^n}) + \frac{F}{(1 + r)^n} $$

where:
- $$ P $$ is the current price of the bond
- $$ C $$ is the annual coupon payment
- $$ r $$ is the yield to maturity
- $$ n $$ is the number of years until maturity
- $$ F $$ is the face value of the bond

Given:
- Face value ($$ F $$) = $1,000
- Annual coupon payment ($$ C $$) = 8% of $1,000 = $80
- Yield to maturity ($$ r $$) = 10% = 0.10
- Number of years until maturity ($$ n $$) = 20 years

Substitute the given values into the formula:

$$ P = \frac{80}{0.10} \times (1 - \frac{1}{(1 + 0.10)^{20}}) + \frac{1000}{(1 + 0.10)^{20}} $$

Now, we can calculate the current price of the bond.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{80}{0.1}\times \left(1-\frac{1}{\left(1+0.1\right)^{20}}\right)+\frac{1000}{\left(1+0.1\right)^{20}}$$
- step1: Add the numbers:
  $$\frac{80}{0.1}\times \left(1-\frac{1}{\left(1+0.1\right)^{20}}\right)+\frac{1000}{1.1^{20}}$$
- step2: Add the numbers:
  $$\frac{80}{0.1}\times \left(1-\frac{1}{1.1^{20}}\right)+\frac{1000}{1.1^{20}}$$
- step3: Convert the expressions:
  $$\frac{80}{0.1}\times \left(1-\frac{1}{\left(\frac{11}{10}\right)^{20}}\right)+\frac{1000}{1.1^{20}}$$
- step4: Simplify:
  $$\frac{80}{0.1}\times \left(1-\frac{10^{20}}{11^{20}}\right)+\frac{1000}{1.1^{20}}$$
- step5: Subtract the numbers:
  $$\frac{80}{0.1}\times \frac{11^{20}-10^{20}}{11^{20}}+\frac{1000}{1.1^{20}}$$
- step6: Divide the numbers:
  $$800\times \frac{11^{20}-10^{20}}{11^{20}}+\frac{1000}{1.1^{20}}$$
- step7: Convert the expressions:
  $$800\times \frac{11^{20}-10^{20}}{11^{20}}+\frac{1000}{\left(\frac{11}{10}\right)^{20}}$$
- step8: Simplify:
  $$800\times \frac{11^{20}-10^{20}}{11^{20}}+\frac{10^{23}}{11^{20}}$$
- step9: Multiply the numbers:
  $$\frac{800\times 11^{20}-800\times 10^{20}}{11^{20}}+\frac{10^{23}}{11^{20}}$$
- step10: Transform the expression:
  $$\frac{800\times 11^{20}-800\times 10^{20}+10^{23}}{11^{20}}$$
- step11: Add the numbers:
  $$\frac{800\times 11^{20}+200\times 10^{20}}{11^{20}}$$
The current price of the bond is approximately $829.73.

Therefore, the correct answer is:
C. $829.73
The current price of the bond is $829.73.

Big House Nursery Inc. has issued 20 - year face value, annual coupon bonds, with a yield to
maturity of . The current price of the bond is
A.
B.
C.
D. There is not enough information to answer this question.

Upstudy AI Solution

Answer

Solution

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Big House Nursery Inc. has issued 20 - year face value, annual coupon bonds, with a yield to maturity of . The current price of the bond is A. B. C. D. There is not enough information to answer this question.

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Big House Nursery Inc. has issued 20 - year face value, annual coupon bonds, with a yield to
maturity of . The current price of the bond is
A.
B.
C.
D. There is not enough information to answer this question.