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Athens wants the European Stability Mechanism (ESM, better known as the bailout fund) to effectively cover the payments Greece owes to the European Central Bank (ECB), according to the Guardian:
Today's three-page plan apparently suggests the ESM buys the €6.7bn of Greek bonds held by the European Central Bank, which mature in July and August.
Here are the payments coming in July (amounts in millions of euros, cumulative amounts on the far right-hand column):
BAML
The IMF payments due in June have now been bundled, and don't have to paid until the end of the month. There's an €85 million ($95.94 million, £62.71 million) payment to the ECB due on 19 June, followed by much bigger ones later in the summer. That includes a July 20 payment worth more than €4 billion.
Greece is already struggling to make much smaller payments than that - even if the government somehow limps past June's IMF payments without defaulting, July 20 seems insurmountable without help.