a$.$ Use a spreadsheet to calculate the durations of the two bonds in Spreadsheet $16\mathrm{.}1$ if the market interest rate increases to $12\%.$ Why does the duration of the coupon bond fall while that of the zero remains unchanged?

$($Hint: Examine what happens to the weights computed in column F$)$

b$.$ Use the same spreadsheet to calculate the duration of the coupon bond if the coupon is $12\%$ instead of $8\%$ and the semiannual interest rate is again $5\%.$ Explain why duration of lower than in Spreadsheet $16\mathrm{.}1($Again$,$ start by looking at column F$)$