General Electric has two bonds outstanding. Both issues have the same credit rating, a face value of $$1,000$ and a coupon rate of $5\%.$ Coupons are paid twice a year. Bond A matures in $1$ year, while bond B matures in $23$ years.

The market interest rate for similar bonds is $8\%.$

a$.$By how much will the price of bond A fall if yields increase to $13\%$ immediately?

b$.$ By how much will the price of bond B fall if yields increase to $13\%$ immediately $($in absolute dollars$)?$