The six$-$month zero rate is $8\%$ per annum with semiannual compounding. The price of a one$-$

year bond that provides a coupon of $6\%$ per annum semiannually is $97.$ What is the one$-$year

continuously compounded zero rate?

A$.8\mathrm{.}02\%$

B$.8\mathrm{.}52\%$

C$.9\mathrm{.}02\%$

D$.9\mathrm{.}52\%$

Answer: C

If the rate is $R$ we must have

or

so that $R=ln(\frac{1}{0\mathrm{.}9137})=0\mathrm{.}0902$ or $9\mathrm{.}02\%.$

The yield curve is flat at $6\%$ per annum. What is the value of an FRA where the holder receives

interest at the rate of $8\%$ per annum for a six$-$month period on a principal of $$1,000$ starting in

two years? All rates are compounded semiannually.

A$.$ $$9\mathrm{.}12$

B$.$ $$9\mathrm{.}02$

C$.$ $$8\mathrm{.}88$

D$.$ $$8\mathrm{.}63$

Answer: D