Suppose you purchase a $10$ year bond with $6\mathrm{.}5\%$ annual coupons. You hold the bond for four years and sell it immediately after receiving the fourth coupon. If the bond's yield to maturity was $5\mathrm{.}2\%$ when you purchased and sold the bond,

a$.$ what cash flows will you pay and receive from your investment in the bond per $$100$ face value?

b$.$ what is the rate of return of your investment?