The policy is not effective until 12:01 AM (if I recall correctly) of the day after the application and payment for the premium is received. Your check is dated 4/20/10 (date of payment), 12:01 AM of the day after receipt and payment would be 4/22/10.
The only way to insure you have insurance in place before closing the loan is to require it to be paid for prior to the closing.
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The opinions expressed are mine and they are not to be taken as legal advice.