$($Caption: The image is a diagram titled "Binomial Interest Rate Tree" showing interest rates for Years $0,1$ and Year $2.$ The interest rates for different scenarios are provided in a tree$-$like structure. In Year $0,$ the number $2\mathrm{.}2500\%$ branches to $3\mathrm{.}5930\%$ and $2\mathrm{.}9417\%$ in Year $1.$ In Year $1,3\mathrm{.}5930\%$ branches to $4\mathrm{.}6470\%$ and $3\mathrm{.}8046\%$ within Year $2.2\mathrm{.}9417\%$ branches to $3\mathrm{.}8046\%$ and $3\mathrm{.}1150\%$ within Year $2)$

On $19$ October $20$X$0,$ Ferguson analyzes the convertible bond issued by Pro Star given in Exhibit $3.$ That day, the option$-$free value of Pro Star's convertible bond is $$1,060$ and its stock price $$37\mathrm{.}50.$

EXHIBIT $3$: Convertible Bond Issued by Pro Star, Inc.

$\backslash$table$[[$Attribute$,$Value$],[$Issue Date,$6$ December $20$X$0],[$Maturity Date,$6$ December $20$X$4],[$Coupon Rate,$2\%$Samuel Samuel

Samuel & Sons is a fixed$-$income specialty firm that offers advisory services to Investment management companies. On $1$ October $20$X$0,$ Steele Ferguson, a senior analyst at Samuel, is reviewing three fixed$-$rate bonds issued by a local firm, Pro Star, Inc. The three bonds, whose characteristics are given in Exhibit $1,$ carry the highest credit rating.

EXHIBIT $1$: Fixed$-$Rate Bonds Issued by Pro Star, Inc.

$\backslash$table$[[$Bond$,$Maturity,Coupon,Type of Bond$],[$Bond #$1,1$ October $20$X$3,4\mathrm{.}40\%$ annual,Option$-$free$],[$Bond #$2,1$ October $20$X$3,4\mathrm{.}40\%$ annual,Callable at par on $1$ October $20$X$1$ and on $1$ October $20$X$2],[$Bond #$3,1$ October $20$X$3,4\mathrm{.}40\%$ annual,Putable at par on $1$ October $20$X$1$ and on $1$ October $20$X$2]]$

The one$-$year, two$-$year, and three$-$year par rates are $2\mathrm{.}250\%,2\mathrm{.}750\%,$ and $3\mathrm{.}100\%,$ respectively. Based on an estimated interest rate volatility of $10\%,$ Ferguson constructs the binomial interest rate tree shown in Exhibit $2.$

EXHIBIT $2$: Binomial Interest Rate Tree

EXHIBIT $2$: Binomial Interest Rate Tree

$($Caption: The image is a diagram titled "Binomial Interest Rate Thee" showing interest rates for Years $0,1$ and Year $2.$ The interest rates for different scenarios are provided in a tree$-$the structure. In Year $0,$ the number $2\mathrm{.}2500\%$ branches to $3\mathrm{.}5930\%$ and $2\mathrm{.}9417\%$ in Year $1.$ In Year $1,3\mathrm{.}5930\%$ branches to $4\mathrm{.}6470\%$ and $3\mathrm{.}8046\%$ within Year $2.2\mathrm{.}9417\%$ branches to $3\mathrm{.}8046\%$ and $3\mathrm{.}1150\%$ within Year $2)$

On $19$ October $20$X$0,$ Ferguson analyzes the convertible bond issued by Pro Star given in Exhibit $3.$ That day, the option$-$free value of Pro Star's convertible bond is $$1,060$ and its stock price $$37,50.$

$($Caption: The image is a diagram titled "Binomial Interest Rate Tree" showing interest rates for Years $0,1$ and Year $2.$ The interest rates for different scenarios are provided in a tree$-$like structure. In Year $0,$ the number $2\mathrm{.}2500\%$ branches to $3\mathrm{.}5930\%$ and $2\mathrm{.}9417\%$ in Year $1.$ In Year $1,3\mathrm{.}5930\%$ branches to $4\mathrm{.}6470\%$ and $3\mathrm{.}8046\%$ within Year $2.2\mathrm{.}9417\%$ branches to $3\mathrm{.}8046\%$ and $3\mathrm{.}1150\%$ within Year $2)$

On $19$ October $20$X$0,$ Ferguson analyzes the convertible bond issued by Pro Star given in Exhibit $3.$ That day, the option$-$free value of Pro Star's convertible bond is $$1,060$ and its stock price $$37\mathrm{.}50.$

EXHIBIT $3$: Convertible Bond Issued by Pro Star, Inc.

$\backslash$table$[[$Attribute$,$Value$],[$Issue Date,$6$ December $20$X$0],[$Maturity Date,$6$ December $20$X$4],[$Coupon Rate,$2\%$ What is the value of Bond number two and Bond number three also all else being equal a rise and interest rates will most likely result in the value of an option embedded in bond three decreasing increasing or remaining unchanged