Juan Rodriguez plans to purchase a home in five years and wants to save up for a down payment. He recently inherited $$25,000$ he can save. He separately examines his budget and determines that he can afford $$500$ per month which he can put into a high$-$yield savings account, independent of the inheritance. That would allow him to use the $$25,000$ for things now and still save up for the down payment. While investigating different investment opportunities, he comes across the following options:

Option $1$: A $5-$year Certificate of Deposit that pays $5\mathrm{.}9\%$ Annual Percentage Rate compounded annually.

Option $2$: A High$-$Yield Savings Account that pays $4\mathrm{.}6\%$ Annual Percentage Rate compounded monthly for a period of $5$ years.

Please answer the following questions.

Part A: If Juan deposits all of his inheritance into the Certificate of Deposit in a lump sum, how much money would be in the account after $5$ years?

Part B: If Juan pays $$500$ a month into the High$-$Yield Savings Account, how much money would be in the account after $5$ years?

Part C: What are the advantages and disadvantages to each of the options? List at least one advantage and one disadvantage for each option. $($Some things you might consider are the total amount deposited, interest earned, flexibility in budget, etc.$)$