Question $3$ On Dec $31,2023,$ you paid $$1,000$ to purchase a bond, which matures on Dec

$31,2026$ with a coupon $5\%($annual$)$ and a face value of $$1,000.$ According to the latest news,

you expect that Fed will maintain the same interest rate $5\%$ in $2024$ with a probability $80\%,$

and decrease the interest rate to $4\%$ with a probability $20\%.$

a$.$ Calculate the $1-$yr rate of return $($Dec $31,2023$ to Dec $31,2024)$ if Fed maintains the

same interest rate.

b$.$ Calculate the $1-$yr rate of return $($Dec $31,2023$ to Dec $31,2024)$ if Fed decreases the

interest rate to $4\%.$

c$.$ Calculate the expected $1-$yr rate of return.