Respuesta :
Answer:
Explanation:
First of all, as the interest is paid semi-annually, we calculate semi-annual interest rate by dividing yield to maturity by the number of periods in a year (2).
Semi-annual interest rate = 0.0818 / 2 = 0.0409
Now using the following formula
[tex]YTM\;=\;\sqrt[n]{\frac{Face\;Value}{Current\;Price}}\;-\;1[/tex]
where,
YTM = 0.0409 (semi-annually)
Face Value = $1000
Current Price = $823.5
n = Number of semi-annual periods
[tex]0.0409\;=\;\sqrt[n]{\frac{1000}{823.5}}\;-\;1\\\\0.0409\;+\;1=\;\sqrt[n]{{1.214}}\\\\1.0409^{n} =\;1.214\\\\[/tex]
Taking natural log on both sides,
[tex]ln(1.0409)^{n} =ln(1.214)\\\\n*ln(1.0409)=ln(1.214)\\\\n=\frac{ln(1.214)}{ln(1.0409)}\\n=4.837[/tex]
Hence, semi-annual periods are 4.837. Therefore, the bond will mature in approximately (4.837/2) 2.4185 years.
