Using the above notation and the no$-$arbitrage opportunity arguments, derive the forward price

in the following cases:

$1.$ Non$-$dividend paying stock

$2.$ Dividend paying stock $($$D$)$

$3.$ Stock with a continuously compounded dividend yield $($d$)$

$1$

$4.$ Commodity with storage costs $($$U$)$

$5.$ Commodity with continuous compounded storage costs $($u$)$

$6.$ Foreign Currency that pays a continuously compounded interest rate rf$,$T $.$ In this case, assume

that S$0$ and FT are prices of $1$ unit of foreign currency in US dollars

$7.$ Forward rate fT$,$T $+$h

For the above derivations, explain in detail all the trades of the arbitrage trading strategy in

all periods. Further, explain how the arbitrage trading strategy will affect prices and restore equilibrium. Note that for commodities, it is usually difficult to short$-$sell the underlying commodity.