A $$50$ stock pays a $$1$ dividend every $3$ months, with the first dividend coming $3$

months from today. The continuously compounded risk$-$free rate is $6\%.$

$($a$)$ What is the price of a prepaid forward contract that expires $1$ year from today,

immediately after the fourth$-$quarter dividend?

$3$

$($b$)$ What is the price of a forward contract that expires at the same time?