猶予 and 期限: granted grace and requested extra time
Distinguish the one-week payment grace period that was granted from extra time requested before a decision, using application and return deadlines as ending-time references.
Granted grace and a request before a decision
「支払い期限に一週間の猶予が与えられた。」 (A one-week grace period was granted for the payment deadline.) 猶予 (ゆうよ) names a grace period or extension. 一週間 gives the length of the grace that was actually granted, and 与えられた reports its grant. The sentence supplies no starting date and does not say that the payment deadline had already passed.
「判断を下す前に、もう少し猶予をください。」 (Please give me a little more time before I make a decision.) The speaker asks for a little more time before making a decision. もう少し supplies no exact number of days, and the request with ください does not establish that the additional time was approved.
The deadlines for submission and return
「申込書は期限までに提出してください。」 (Please submit the application by the deadline.) 期限 (きげん) names a deadline or time limit. 期限までに marks the ending-time reference for submitting the application. The sentence requests submission; it does not report that submission was completed.
「返却期限を忘れないよう手帳に書いた。」 (I wrote the return deadline in my notebook so I would not forget it.) 返却期限 is the return deadline. The completed action is writing that deadline in a notebook to avoid forgetting it. This does not establish that the item was returned.
Check whether the additional time was allowed
The payment sentence reports an actual one-week grant of 猶予. The decision sentence asks for more 猶予. Keep those statuses separate even though both use the same noun for additional time.
期限 gives the deadline against which a submission or return is considered. For 猶予, the useful question in these examples is whether extra time was granted or merely requested, followed by any duration the sentence actually supplies.
Were both the one-week payment grace period and the extra time before a decision approved?
Show the answer and why
The payment sentence says that a one-week grace period was granted. The decision sentence only requests a little more time; it gives neither an exact duration nor an approval.