Answer:
Number of years = 7.54 or 8 years
Explanation:
We know,
YTM = [tex]\frac{I + \frac{M - V_{o}}{n} }{\frac{2M + V_{o} }{3}}[/tex]
Here,
I = Coupon payment
M = Par value
V = Market price
Given,
M = Par value = $1,000
V = Market price = $1,119.34
I = Coupon Payment = Par value × Coupon rate = $1,000 × 6.4% = $64
Since, it is a semi-annual payment = $64/2 = $32
YTM = 4.6%
Therefore, putting the value into the above formula, we can get
YTM = [tex]\frac{32 + \frac{1,000 - 1119.34}{n} }{\frac{(2*1,000) + 1,119.34}{3}}[/tex]
or, 0.046 = [tex]\frac{\frac{32n - 119.34}{n} }{\frac{3,119.34}{3}}[/tex]
or, 0.046 = [tex]\frac{\frac{32n - 119.34}{n} }{1,039.78}[/tex]
or, 47.82988 = [tex]\frac{32n - 119.34}{n}[/tex] [Multiplying both the sides by 1,039.78]
or, 47.82988n = 32n - 119.34 [Multiplying both the sides by n]
or, 47.82988n - 32n = -119.34
or, -15.82988n = -119.34
or, n = (-119.34) ÷ (-15.82988)
Therefore, n = 7.54 years or almost 8 years.
