If I put money into a savings account that gains interest, will it compound?
Answer:
Yes, they compound monthly. The Roth IRA is not a specific investment vehicle (like a savings account or mutual fund), but rather a kind of account.
If you owned cash in a money market fund inside of a Roth IRA, you'd probably do best in the long run, because the cash would compound every month (or more often, depending on the account), and when you withdrew it you would not owe taxes on it. Conversely, a cash savings account generates interest that is taxable every year, whether or not you withdraw it.
Yes, you will earn interest on your interest each month.
Yes. You'll earn interest every month that you have money in the account. A savings account is protected by the FDIC so you won't lose any money where as a Roth IRA isn't.
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