Bonds A$,$ B$,$ C$,$ and D have face values of $$1,000\mathrm{.}00,$ pay semi$-$annual coupons with the next coupon due in $6$ months, and mature in T years. Bonds A and B have different coupon rates, and bonds C and D have different yields$-$to$-$maturity. Which assertion is true if PA $>$ PB $>0,$ PC $>$ PD $>0,$ T $>0,$ Y $>0,$ and C $>0?$ Note that all bonds with a time$-$to$-$maturity of T have the same time$-$to$-$maturity, all bonds with a yield$-$to$-$maturity of Y havethe same yield$-$to$-$maturity $($YTM$),$ and all bonds with a coupon rate of C have thesame coupon rate.

Bond Bond Price Time$-$to$-$maturity Yield$-$to$-$maturity

A PA T Y

B PB T Y

Bond Bond Price Time$-$to$-$maturity Coupon rate

C PC T C

D PD T C

Bond A has a higher coupon rate than bond B and bond D has a higher YTM than bond C

Bond B has a higher coupon rate than bond A and bond D has a higher YTM than bond C

Bond B has a higher coupon rate than bond A and bond C has a higher YTM than bond D

Bond A has a higher coupon rate than bond B and bond C has a higher YTM than bond D