Big House Nursery Inc. has issued 20 - year \( \$ 1,000 \) face value, \( 8 \% \) annual coupon bonds, with a yield to maturity of \( 10 \% \). The current price of the bond is A. \( \$ 1,196.36 \) B. \( \$ 1,000.00 \) C. \( \$ 829.73 \) D. There is not enough information to answer this question.

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