$4.$ A $10-$year US Government bond with face value of $$1,000$ pays a yearly coupon of $4\mathrm{.}125\%.$

a$.$ Calculate the present value of each coupon payment from year $1$ to year $10.$

b$.$ If this bond sells today for $$850($present value$),$ what is the yield if there were no coupons?

c$.$ What is the overall yield considering it also pays yearly coupons?