Is there is a type of account where I can deposit money whenever I want, but can only withdraw it after a certain time?
Two or three account types come to mind. You'll need to decide if they meet your needs and find out if they are available in your area.
The first is the club account. Christmas Club, Holiday Club, Vacation Club. They get labeled in lots of different ways. Some banks have them, and others don't. Some that have them will only allow automatic charges to other accounts within the bank, for funding. Others may permit deposits on your own schedule. All typically pay out at a predetermined time, often electronically to another account in the same bank.
The second is what we used to call a time deposit open account. These allow deposits at any time, but require advance notice for any withdrawal. This type of account is not offered by many banks, but you may find one that does.
Finally, you may find a bank that offers time deposits (certificates of deposit) that permit additions, but no withdrawals (except with a penalty) before maturity.
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