Answer:
Annual YTM = 2.824%
Semi Annual YTM = 1.402%
Explanation:
Semi - Annual YTM
We know,
Expected YTM (Semi-annual) = [tex]\frac{I + \frac{M - V_{0}}{n}}{\frac{M + V_{0}}{2}}[/tex]
Given,
I = Coupon payment = Coupon rate × Bond Par value = $1,000 × 4.80% = $48
Semiannual coupon payment = $48/2 = $24
M = Bond Par value = $1,000
Vo = Market value of Bond = $1,175
n = number of years (period) = 20
Putting all the values into the formula, we can get,
Expected annual YTM = [tex]\frac{24 + \frac{1,000 - 1,175}{20}}{\frac{1,000 + 1,175}{2}}[/tex]
or, expected annual YTM = [tex]\frac{24 - 8.75}{1,087.5}[/tex]
or, YTM = 0.01402
Therefore, semiannual YTM = 1.402%
Annual Expected YTM = 2 × 0.01402 = 0.02804 or, 2.804%
Therefore, annual YTM = (1 + Semiannual YTM)^2 - 1
or, annual YTM = (1 + 0.01402)^2 - 1
annual YTM = 0.02824
Therefore, annual YTM = 2.824%
