Calculate yield to maturity, current yield. and capital gains yield for the following bonds

a$.$ An $8$ percent coupon bond with a $$1,000$ face value and $10$ years remaining to

maturity. The bond, which pays quarterly coupons, is selling at $$922\mathrm{.}09.$

b$.$ A $9$ percent coupon bond with a $$1,000$ face value and $15$ years remaining to

maturity. The bond, which pays annual coupons, is selling at $$1,041\mathrm{.}52.$

c$.$ Calculate the duration and modified duration for EACH of the two bonds in parts

a and b $.$