Respuesta :
Answer:
option (C) - 6.11%
Explanation:
Data provided :
Coupon rate one year ago = 6.5% = 0.065
Semiannual coupon rate = [tex]\frac{0.065}{2}[/tex] = 0.0325
Face value = $1,000
Present market yield = 7.2% = 0.072
Semiannual Present market yield, r = [tex]\frac{0.072}{2}[/tex] = 0.036
Now,
With semiannual coupon rate bond price one year ago, C
= 0.0325 × $1,000
= $32.5
Total period in 15 years = 15 year - 1 year = 14 year
or
n = 14 × 2 = 28 semiannual periods
Therefore,
The present value = [tex]C\times[\frac{(1-(1+r)^{-n})}{r}]+FV(1+r)^{-n}[/tex]
= [tex]\$32.5\times[\frac{(1-(1+0.036)^{-28})}{0.036}]+\$1,000\times(1+0.036)^{-28}[/tex]
or
= $32.5 × 17.4591 + $1,000 × 0.37147
= $567.42 + $371.47
= $938.89
Hence,
The percent change in bond price = [tex]\frac{\textup{Final price - Initial price}}{\textup{Initial price}}\times100\%[/tex]
= [tex]\frac{\textup{938.89-1,000}}{\textup{1,000}}[/tex]
= - 6.11%
therefore,
the correct answer is option (C) - 6.11%
