When a one-time coupon is applied to a subscription at the time of sign-up, the discount will be applied only to the charges collected on sign-up. Whereas when a limited period 1-month coupon is applied to a subscription at sign-up, the discount will be applied to the sign-up charges and to any other charge that is added within the one month period.
In both the cases, only charges for the first month will have the discount applied. If you add any charge for the second month, the discount will not be applied.
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