Consider two semi$-$annual coupon bonds with the following properties:

Bond Maturity Face Value Coupon

B$13$ years $10012\%$

B$23\mathrm{.}5$ years $10030\mathrm{.}3525\%$

The current yield for both bonds is $10\%.$The current yield for both bonds is $10\%.$

$($i$)$ Compute the durations of the two bonds, and verify that they are equal.

$($ii$)$ By computing the prices $($B$1$ and B$2),$ determine the value of $n$ that makes $nB1=B2.$

$($i$)$ Compute the durations of the two bonds, and verify that they are equal.

$($ii$)$ By computing the prices $($B$1$ and B$2),$ determine the value of n that makes nB$1=$ B$2.$