$.$ Assume an asset sells in the spot market for a price of $$90,$ the risk$-$free rate is $3\%,$ and the forward contract expires in $9$ months. What is the initial value of the contract and the correct forward price?

b$.$ Using the forward contract from part a$,$ the underlying price is $$94$ three months later. Now what is the value of the contract?

c$.$ Assume an asset sells in the spot market for a price of $$90.$ The risk$-$free rate is $3\%,$ and the forward contract on the asset expires in $9$ months. The asset pays a dividend of $$1$ and storage costs are $$2$ a year, both of which are in present value form. What is the correct forward price?

d$.$ Using the forward contract from part c$,$ the underlying price is $$94$ three months later. Now what is the value of the contract?