PV vs BAC

How does Planned Value (PV) differ from Budget-at-Completion (BAC)? Suppose you have a scheduled project activity with a total duration of 12 weeks and an activity budget of $1,200. Assuming the planned expenditure rate is constant throughout the activity duration, what is PV at the end of the fourth week? At the end of the tenth week? At the end of the twelfth week?

Suppose now the planned expenditure rate is: $50 for each of the 1st two weeks; $100 for each of the 3rd and 4th weeks; $125 for each of the 5th and 6th weeks; $150 for each of the 7th and 8th weeks; $125 for week 9; and $75 for each of weeks 10 through 12. What is PV at the end of the fourth week? At the end of the tenth week? At the end of the twelfth week?