Richard Plodhavens owns a British Consul, a security which pays the equivalent

of $$3000$ U$.$S$.$ each year on February $1,$ forever. Richard has recently considered

selling the security. The current interest rate is $6\%$

a$.$ What is the minimum sales price he must be offered to should consider

selling the Consul, after February $1?$

b$.$ Joe Miller offers to purchase the Richard's Consul, but wants to buy it on

January $30.$ Should Joe change his price in $($a$)?$ If so$,$ why and what price

should he offer?