Porsche plans on introducing a new four$-$door luxury automobile in $2023$ called the Panamera X$.$ Although pricing has not been set, some automotive analysts believe the basic production model will be sold in Europe at a price of $120,000.$ At this price they believed the company stands to earn a $20\%$ margin on each car.

a$.$ If the spot rate in $2023$ was $$1\mathrm{.}4400/,$ what would be its projected price in the United States?

b$.$ If the price in the US market was set at $$158,000,$ and the spot exchange rate averaged $$1\mathrm{.}4240/,$ what would be the margin on the Panamera X$?$

c$.$ What would the price in the US market have to be in order to keep the profit margin at $20\%$ despite the dollar appreciation.