Question $4$ You are planning to attend an master level Program that will require payment of $\backslash (\backslash$$ $12,000\backslash )$ a year in tuition expenses at the end of each year for $2$ years. Bonds currently yield $5\backslash \%.$ a What is the present value of your obligation Blank $1?($ sample answer: $25000)$ b What is the duration of your obligation Blank $2?($sample answer: $2\mathrm{.}53$ years c Suppose you wish to fund your obligation using $1-$year zero$-$coupon bonds and perpetuity bonds. How much of $1-$year zero in dollarBlank $3($input example: $25000)$ and in percentage Blank $4($input example: $34\mathrm{.}7\backslash \%)$ and how much of perpetuity bonds in dollar Blank $5($sample answer: $25000)$ and in percentage Blank $6$ will you want to hold to both fully fund and immunize your obligation? Suppose you buy $1-$year zero$-$coupon bonds and perpetuity bonds to immunize your obligation. Now suppose that rates immediately increase to $\backslash (6\backslash \%\backslash ).$ e$.$ What is your tuition obligation Blank $7$ now? $($sample answer: $\backslash (\backslash$$ $25,000\backslash ))$ f$.$ What is the value of your position in $1-$year$-$zero$-$coupon bonds now Blank $8?($sample answer: $25000)$ g$.$ What is the value of your position in perpetuity now Blank $9?($sample answer: $25000)$