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Question:
Find the value of a ₱ 20,000.00 bond with interest of 14% compounded semi-annually which is redeemable at 108% in 5 years that yields the purchaser 6% converted semi-annually.
Solution:
[tex]F_{v}[/tex] = Face Value = ₱ 20,000.00
[tex]r_{b}[/tex] = bond rate = 0.14
m = number of conversion period per year = 2
t = term = 5 years
[tex]r_{y}[/tex] = yield rate = 0.06
b = periodic bond rate = [tex]\frac{0.14}{2} = 0.07[/tex]
n = total number of conversion period = 5(2) = 10
i = periodic rate = [tex]\frac{0.06}{2} = 0.03[/tex]
Substitute these values to compute the following:
Common payment = [tex]c_{p}[/tex] = (20,000)(0.07) = ₱ 1,400
Redemption Value = [tex]R_{v}[/tex] = (20,000)(1.08) = ₱ 21,600
Purchase Price:
[tex]p = R_{v}(1+i)^{-n}+c_{p}[\frac{1-(1+i)^{-n} }{i} ][/tex]
[tex]p = (21,600)(1+0.03)^{-10} + 1,400[\frac{1-(1+0.03)x^{-10} }{0.03}[/tex] = ₱28,014.17
Therefore, the investor who pays ₱28,014.71 is investing the money.