Answer:
Market Price $985.01
Explanation:
We have to convert the US semiannually rate to annually.
[tex](1 + 0.078/2)^{2} -1 = 0.079521[/tex]
Now this is the annual rate spected for a similar US Bonds
So we are going to calculate the present value using this rate.
Present value of an annuity of 78 for 20 years at 7.9521%
[tex]C * \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
[tex]78 * \frac{1-(1+0.079521)^{-20} }{0.079521} = PV\\[/tex]
PV = 768.55
And we need to add the present value ofthe 1,000 euros at this rate
[tex]\frac{Principal}{(1 + rate)^{time} = Present Value}[/tex]
[tex]\frac{1,000}{(1 + 0.079521)^{20} = Present Value }[/tex]
Present Value = 216.4602211
Adding those two values together
$985.01
The reasoning behind this is that an american investor will prefer at equal price an US bonds because it compounds interest twice a year over the German Bonds.
