Today is January $1,2024.$ Your friend Joe has just signed a contract to play for a baseball team. He will receive

$$900,000$ for $2024,$ $$1,000,000$ for $2025,$ $$1,100,000$ for $2026,$ and $$1,200,000$ for $2027.$ All payments are made at

the beginning of the year. Assume $8\%$ annual interest rate $($EAR$).$

a$.$ What is the present value of his contract?

b$.$ If instead of increasing annual payments Joe wants equal dollar amount month$-$end cheques, how large is

his monthly pay $($assuming the present value remains the same$)?$