Consider a $15-$year fully amortizing mortgage with a note rate of $8\%,$ priced at $98-13.$ Amortize the mortgage assuming that the borrower does not curtail the loan, nor defaults, and pays off the entire balance at the end of year $6($immediately after the last regular payment$).$ There is no prepayment penalty. Use the relevant cash flows to the lender to compute the average life, the duration, and convexity of this note, all in years or years$-$sq$.$