You would have to report it as income if you had the right of possession- (based on the limited facts) essentially in the first case, you did not have income because it was your parent's money. In the second case, it would still be income even though it was left in the account overseas because you were the only account holder and you could have (even if you did not) taken the money out. With the first account, even though you could have taken the money out (by rights as an account holder) because your parents are also able to, it is different. Also, for the first (shared account) if the money was originally that of your parent's (as opposed to you and they putting the money in) the interest earned resulted from their contribution. For an account in your name only, it was your money that earned the income, so it is your income.
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