Respuesta :
Answer:
(a) 9.9%
(b) 10.09%
The further explanation is given below.
Explanation:
The given values are:
Coupon payment
= $99
Price
= $1,000
(a)
The Yield to maturity (YTM) will be:
= [tex]\frac{C+\frac{F-P}{n} }{\frac{F+P}{2} }[/tex]
where,
C = Coupon payment
P = Price
n = years to maturity
F = Face value
On putting the estimated values is the above formula, we get
⇒ [tex]99+\frac{0}{1000}[/tex]
⇒ [tex].099[/tex]
⇒ [tex]9.9[/tex]%
(b)
Although the 1st year coupon was indeed reinvested outside an interest rate of r%, cumulative money raised will indeed be made at the end of 2nd year.
= [tex][99\times (1 + r)] + 1,099[/tex]
Came to the realization compound YTM is therefore a function of r, as is shown throughout the table below:
Rate (r) Total proceeds Realized YTM ([tex](\frac{proceeds}{1000} )^{.5} - 1[/tex])
7.9% 1205.8 9.8%
9.9% 1207.8 9.9%
11.9% 1209.8 9.99%
Now,
Overall proceeds realized YTM:
= [tex]\frac{proceeds}{1000} -18 \ percent \ 1,\frac{2081208}{1000} - 1[/tex]
= [tex]0.0991[/tex]
= [tex]9.91 \ percent \ 10 \ percent \ 1,\frac{2101210}{1000}- 1[/tex]
= [tex]0.1000[/tex]
= [tex]10.00 \ percent \ 12 \ percent \ 1,\frac{2121212}{1000}-1[/tex]
= [tex]0.1009[/tex]
= [tex]10.09[/tex]%