Use the following information for Questions $610$:

Table of Interest Rates:

Time Period Rate

$0$y$1$y $3\mathrm{.}00\%$

$0$y$2$y $4\mathrm{.}80\%$

$0$y$3$y $6\mathrm{.}30\%$

$1$y$1$y $6\mathrm{.}63\%$

$2$y$1$y $9\mathrm{.}37\%$

Consider the following bond:

$$ Exactly $3$ years to maturity

$9\mathrm{.}7\%$ coupon rate, paid annually

$$ $$100$ par value

$$ Bond is callable in exactly $1$ year for $101\mathrm{.}5$ and exactly $2$ years for $100\mathrm{.}5.$

$6.$ Suppose that there is zero volatility in interest rates. Restated, suppose that future interest

rates equal current market expectations. What is the price of the callable bond? Round your

answer to three decimal places.

$7.$ Now suppose that future interest rates are uncertain. Specifically, there is $15\%$ volatility

in underlying interest rates with $50/50$ likelihood that the rate increases or decreases. The

rates evolve as follows:

What is the price of the callable bond in this scenario per $100$ of par value? Round your

answer to three decimal places.

Rate from t $=0$ to t $=1$ Rate from t $=1$ to t $=2$ Rate from t $=2$ to t $=3$

$3\mathrm{.}00\%$

$7\mathrm{.}63\%$

$5\mathrm{.}65\%$

$6\mathrm{.}82\%$

$9\mathrm{.}21\%$

$12\mathrm{.}43\%$