It is April $1.$ A US company expects to receive $30$ million Japanese yen at the end of September. Yen futures contracts on the CME Group have delivery months of April, July, October, and January. One contract is for the delivery of $10$ million yen. We suppose that the futures price on April $1$ in cents per yen is $0\mathrm{.}9750$ and that the spot and futures prices when the contract is closed out are $0\mathrm{.}9150$ and $0\mathrm{.}9200,$ respectively.

What delivery month is suitable for this company?

How much is the total price paid by the company?