$22.$ Two annual coupons bonds both mature in $6$ years. Bond A has a coupon rate of $4\mathrm{.}00\%$ and a yield to maturity of $8\mathrm{.}00\%.$ Bond B has a coupon rate of $8\mathrm{.}00\%$ and a yield to maturity of $4\mathrm{.}00\%.$

Select one of the following statements that is true about Bond A and Bond B$.$

Bond A is $$815\mathrm{.}08$ greater than Bond B

The price difference between Bond A and Bond B is $$2024\mathrm{.}77$

The price difference between Bond A and Bond B is $$394\mathrm{.}60$

Bond B is $$1209\mathrm{.}69$ greater than Bond A

All of the Above