$1.$ You are researching two different loan opportunities for a business opportunity. You plan to borrow $$10,000$ for a period of $5$ years. Calculate the total payment amount for both offers below.

Offer one: $6\%$ APR compounded once a year.

Show your math. Important: Keep all decimal numbers in your calculation until the end, then round to the nearest cent.

Offer two: $4\mathrm{.}5\%$ APR compounded once a month.

Show your math. Important: Keep all decimal numbers in your calculation until the end, then round to the nearest cent.

$2.$ Which offer should you take? Explain referencing specific details from your above calculations.

$3.$ Based on your results, is it better to seek out loans with less frequent compounding or lower interest rates?

Explain your choice.