Property owners who are 65 years of age or older are eligible to receive a discount on their yearly home taxes called, the homestead exemption. The amount of the discount is subtracted from the recorded assessed value of the property to arrive at the new adjusted assessment value of the home. This becomes the final number that is then used to compute the yearly taxes. The yearly tax is the calculation of the adjusted assessed value of the home x whatever is the current year's tax rate. For instance, if your current assessed value of your home is $150,000 and the homestead reduction is $35,000 then your new adjusted assessed home value would be $150,000 - $35,000 = $115,000. You would then use $115,000 x the current tax rate for your area to come up with adjusted tax amount for that year.
No matter what month of the year you turn 65, as long as you are 65 at some point in that year (including Dec 31st) then you can take advantage of the exemption for that entire year as long as you fill out the appropriate Homestead Exemption application form (forms are included below) and be sure to send it into you local PVA in a timely manner. If you are married, as soon as either spouse turns 65, you are also eligible for this deduction.
Since the Homestead Exemption amount will likely increase every year, you would need to check with your county to know exactly what that year's discount is. See below for the links to access this info and the application forms to apply. Once you have applied you will be good for as long as you own that property. You will not need to reapply every year for the Homestead Exemption, as your future tax calculations will always include the exemption. However, should you buy a new home, you will need to reapply for the exemption on your new property.