$2$ Darius has $$25000$ to invest. He has two investment options:

$$ Bank A offers to pay $8\mathrm{.}2\%$ per annum compounding six$-$monthly

$$ Bank B offers to pay $8\mathrm{.}1\%$ per annum compounding quarterly

Darius would like his money to remain invested for a period of $18$ months.

a Which of the two investment options would earn Darius the most interest? Justify your answer by explaining how you compared the two investment options.

b Calculate the difference between the total interest earned by both investment options. Round your answer to the nearest dollar.

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