A Pension Puzzle For You

[sunny-dave]

Your Pension Provider pays you every four weeks - rather than every calendar month.

They offer a bonus double payment whenever your pension is due to be paid exactly on your birthday.

Assuming you get the first double-bubble on your 65th birthday, what is the earliest age at which you will next get the bonus? What is the latest?

You can assume they make payments every day of the year as necessary - no need to fuss over weekends or Bank Hols.

You can ignore 'leap day babies' as they just won't live long enough.

Quizzy Dave.

[pixie374]

4 weeks after your 65th birthday? Or I am missing something...

[brainiac]

I'm afraid I don't know the answer to that, dave (is it the theme of the latest Listener?), but on the subject of pensions, I have been wondering if one gets paid one's first state pension a bit before turning 66? I couple of friends seem to have received it that much early.

[sunny-dave]

You are missing the point Pixie - you'll get a standard payment every four weeks - I'm asking when you'll next get the the "bonus double on your birthday" payment.

[sunny-dave]

Brains - the first state pension payment is a lottery depending on what day of the week you are born - I got mine a few days after my 65th - others a few days before.

[bhg481]

The calendar repeats itself roughly every 13 years, depending how leap years fall. In other words this year's calendar will probably work for 2033 but I haven't checked. Actually, it won't, because this year is a leap year and 2033 won't be, but it's about that sort of frequency.

[brainiac]

Monday's child is fair of face....

[sunny-dave]

Not that easy bhg - you need to consider the 28 day frequency of the payments.

[bhg481]

sd - yes, I was thinking my birthday was on the same day of the week approximately every 13 years but, of course, since the pension will be paid every 4 weeks it will be about every 52 years.

[sunny-dave]

Not quite so long, bhg - you may live to get the bonus ...

[bhg481]

sd - what's your thought?

[sunny-dave]

I've worked it all out - I'm waiting to see if any of our maths puzzlers can bottom out the conundrum too, before I give the answers later.

[petland]

Google Calendar 1950 - 2060 - Seattle Pacific University and find the date of your 65th birthday, the chart will reveal every year the day will repeat.

[bhg481]

petland - that was my initial mistake; you're only paid every 4 weeks, so the fact that your birthday was on a Sunday in 1950 and in 1956 doesn't mean that that was a pension day.

[THECORBYLOON]

Are you ignoring leap years completely?

[THECORBYLOON]

If yes, I reckon it's twenty-eight years.

[sunny-dave]

Not ignoring leap years - just the poor *** born on Feb 29th :)

It would be every 28 years - but allowing for leap years it is ... more complicated :)

[THECORBYLOON]

It's twenty-three years.

[sunny-dave]

It's a surprisingly difficult question, TCL - I eventually used brute force (ie a spreadsheet) to show that the next double payment would be in either 22, 23 or 45 years depending on how your 65th falls with respect to the leap year cycle - I'd be cross at having to live to 110 to get my bonus!

[THECORBYLOON]

I used a spreadsheet starting on 29.2 20 and used 1st March as the birthday in non-leap years.

[THECORBYLOON]

What birthday gives the answer as forty-five years?