Problem $2$: Present Value $[6$ Points$]$ Consider a bond that you could buy. This bond pays out $\backslash (\backslash$$ $4,000\backslash )$ four years from now. This bond also pays a coupon payment of $\backslash (\backslash$$ $200\backslash )$ two years from now and a second $\backslash (\backslash$$ $200\backslash )$ payment three years from now. The interest rate of $\backslash (10\backslash \%\backslash ).10.$ What is the Present Value of the payments from this bond? $[2$ points$]$ Now suppose that at the beginning of two years from now $($before the first coupon payment is given out$),$ this individual has an option to not receive their second coupon payment, and instead increase their first coupon payment to $\backslash (\backslash$$ $350\backslash ).11.$ Should this individual take this option? $[2$ points$]$ Finally, suppose that this individual can buy this bond, including its coupon payments and the option, for a price of $\backslash (\backslash$$ $3,200\backslash ).12.$ What would be the present value of the benefits of this bond minus the present value of the costs of this bond, assuming that this bond includes the option from Q$11?$ Should this individual buy this bond? $[$Hint: This is called the Net$-$Present Value $($NPV$)][2$ points$]$