Question

What is the market value of a bond that has a 6 % coupon paid semiannually , has a $ 2,000 face value , has 15 years to maturity and has a 4 % yield to maturity . Write down the formula with appropriate numbers inserted to solve the problem along with the correct answer .

Answer 1

Face value of Bond (F) = $2,000

Coupon rate = 6%

Coupon frequency = semiannually

Semiannual Coupon Amount(C) = 3%*2000= $60

Semiannual Yield to maturity (r) = 4%/2 = 2%

Years to maturity = 15

Coupon periods to maturity(n) = 15*2 = 30

Price of Bond can be computed with following equation:

$\large P = C*(P/A,r,n)+F*(P/F,r,n)$

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

putting the values:

$P = 60*\frac{(1+0.02)^{30}-1}{0.02*(1+0.02)^{30}}+2,000*\frac{1}{(1+0.02)^{30}}$

$P = 60*\frac{1.81136158410335-1}{0.02*1.81136158410335}+\frac{2,000}{1.81136158410335}$

$P = 60*\frac{0.81136158410335}{0.0362272316820671}+1104.14177795982$

$P = 60*22.3964555510044+1104.14177795982$

$P = 2447.92911102008$

$\bg_green \large P = \$2,447.93$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.