a$.$ The $8\mathrm{.}1\%,$ twenty$-$year bond yields $6\mathrm{.}1\%.$ If this yield to maturity remains unchanged, what will be its price one year hence?In November $2020,$ Treasury $45/8$s of $2042$ offered a semiannually compounded yield to maturity of $2\mathrm{.}74\%.$ Recognizing that

coupons are paid semiannually, calculate the bond's price. Assume face value is $$1,000.$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Bond price

Assume annual coupon payments and a face value of $$1,000.$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ What is the total return to an investor who held the bond over this year?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.