A European bond pays interest annually while a comparable U.S. Bond
pays interest semi-annually (other than the periodic interest payment,
all other characteristics of the bonds are the same). If the European
Bond pays 11 percent, what is the rate on the U.S. Bond that maintains
interest rate parity between the two bonds?

Hi bluesteel!
This problem can be solved in the following way. If the interest rate
parity holds, then both bonds should end up having the same payoff.
Consider the European bonds. If you invest $x in European bonds today,
you will have

Now                     In one year
 x                   x*(1+0.11)=x*(1.11)

If you invest in US bonds, you will receive a payment six months from
now. You could then reinvest this payment in US bonds and receive
another payment one year from now, which will be higher than the first
one because the investment has grown. Let's call 'r' to the rate of
the semi-annual payment. Specifically, you will have

 Now       In six months              In one year
  x           x*(1+r)            x*(1+r)*(1+r)=x*(1+r)^2


So, for the interest rate parity to hold, it must be the case that the
same investment should produce the same results for both bonds. So we
must solve the following equation:

x*(1.11) = x*(1+r)^2

that is, we equalize the returns of both bonds after one year. From
this equation we get:

1.11 = (1+r)^2
1+r = sqrt(1.11)
r = sqrt(1.11) - 1
r = 0.0535...

So we now know that the US bond must make payments of 5.35% every six
months for th interest rate parity to hold. Therefore, we say that the
US bond pays has an annual interest rate of 10.7% (5.35*2), paid
semi-annualy.

This answer makes sense intuitively. We should expect the US bond to
earn a lower interest rate (US 10.7% vs European 11%), because they'll
let you have a portion of the annual payment earlier in the year.
Similarly, the annual interest rate of a bond that paid quarterly or
monthly would be even lower.


I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request clarification before rating it; otherwise I
await your rating and final comments.

Best wishes!
elmarto

Great answer. More than just the solution, I appreciate the
explanation; now I understand the answer.