The current term structure of interest rates is flat at $3\mathrm{.}23\%,$ and is expected to shift up$.$ You have locked into a

long$-$term lease on a real estate in Cambridge to pay $$1$ million a year forever, starting $3$ years $(t=3)$ from

now $(t=0).$

Use the above information to answer questions $($A$)-($C$).$

A$.$ What is the present value of this liability?

B$.$ What is the modified duration of this liability? $($Hint: You need to use the definition of modified duration and differentiate the price $($i$.$e$.,$ present value$)$ of this liability.$)$

C$.$ Suppose that immediately after you signed the lease, the interest rate moves up by $0\mathrm{.}68\%$ for all maturities. Using the modified duration, by how much has your liability from the lease changed? $($Enter a negative number if decreasing.$)$