Consider a hybrid $($gas$-$electric$)$ vehicle with a sticker price of $$31,500.$ This vehicle will average $30$ miles per gallon of gasoline. A tax credit of $$1,500$ for the hybrid vehicle is being awarded and thus it effectively reduces its sticker price to $$30,000.$ A comparably equipped gasoline$-$only vehicle will cost $$28,000$ and will average $25$ miles per gallon of gasoline.

a$)$ Assuming gasoline costs of $$4\mathrm{.}00$ per gallon, an interest rate of $3\%$ per year and a study period of five years, find the breakeven mileage per year between the hybrid vehicle and the gas$-$only vehicle.

b$)$ What is the recommended vehicle to purchase if the total mileage per year equals $20,000$ miles?