Your local bank is offering a new type of retirement savings account. An initial deposit is made to the account when it is opened. This money and any accumulated interest must be left in the account for $28$ years. No additional deposits can be made. On the day the account is opened and on each annual anniversary of the initial deposit, the account balance is reviewed and the following terms apply:

If the account balance is less than or equal to $$20,000,$ interest for the next annual period is $7\frac{\%}{?}$ year compounded annually.

If the account balance is greater than $$20,000$ but less than or equal to $$40,000,$ interest for the next annual period is $10\frac{\%}{y}$ear compounded quarterly.

If the account balance is greater than $$40,000,$ interest for the next annual period is $12\%/$year compounded monthly.

You decide to open an account under these terms today with $$9,400.$ How much money will you withdraw when the account is closed $28$ years from today?

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