You will be paying $$12,500$ a year in tuition expenses at the end of the next two years. Bonds currently yield $9\%.$ Required: a$.$ What are the present value and duration of your obligation? $($Do not round intermediate calculations. Round "Present value" to $2$ decimal places and "Duration" to $4$ decimal places.$)$ Problem $11-15($Algo$)$

You will be paying $$12,500$ a year in tuition expenses at the end of the

next two vears Rnds currently yield $9\%.$

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Required:

a$.$ What are the present value and duration of your obligation?

Note: Do not round intermediate calculations. Round "Present value"

to $2$ decimal places and "Duration" to $4$ decimal places.

b$.$ What is the duration of a zero$-$coupon bond that would immunize your

obligation and its future redemption value?

Note: Do not round intermediate calculations. Round "Duration" to $4$

decimal places and "Future redemption value" to $2$ decimal places.

c$.$Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to $10\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation?

d$.$Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates immediately falls to $8\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and that of your tuition obligation?