In the fixed income market, there are two types of bonds:

$1.$ Bond A:

$$ Newly issued coupon bond

$$ Fixed coupon rate $=5\mathrm{.}0\%$

$$ Nominal value $=1000$ Euros

$$ Maturity period $=6$ years from today

$$ Redeemed in the form of annuity payments, with the first payment one year from now

$$ Current market price: $1023\mathrm{.}79$ Euros

$2.$ Bond B:

$$ Perpetual bond

$$ Next coupon payment of $45$ Euros to be made in one year

$$ Coupon payments will decrease by $0\mathrm{.}50\%$ each year

$$ What is the duration of Bond B$?$