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.

[Tilly2]

Sorry to be a bit dense here Dave, but is this a hypothetical conundrum or does this pension bonus actually occur?

[sunny-dave]

Hypothetical, tills, - just a maths problem

[sunny-dave]

Try 1st March 2022, TCL

[sunny-dave]

Sorry 1st March 2021

[gness]

It's been a wet day here but this has kept Dave happily occupied...... :-)

[pixie374]

As long as it kept him quiet for a bit :-)

[gness]

Quiet? Not a chance, Pixie. He kept finding me and explaining more...with leap years...without leap years....I was..... fascinated..... :-(

[pixie374]

I'm sure.... lol. I hope your afternoon was more interesting than his :-) xx

[pixie374]

Dave, 28 years is my working... please relax and do something with gness :-)

[Jonathan-Joe]

We might as well assume that one year in every four is a leap year. We can ignore the fact that century years not divisible by 400 are not leap years as very few living saw the year 1900 and I doubt any current pensioner expects to see 2100!
The answer cannot be 28 years as this period has (21 x 365) + (7 x 366) = 10227 days which is not a multiple of 28.

[Jonathan-Joe]

Should have included this in my previous response. There will be more than one answer depending on whether the next leap day after first payment is within one, two, three or four years.

[sunny-dave]

Correct J-J - as I said on the previous page, the relevant period is either 22, 23 or 45 years, depending on where we are in the leap year cycle when the recipient hits 65.

[choux]

Gness, should you not tell Dave that there are lockdown easements in Ireland now? ;)

[gness]

Ahh, Choux...after doing the right thing...as were all our friends and neighbours we were just venturing out into our village in what has become known as Ireland's safe county when the Americans arrived in droves....and some entitled Dubs of course.
Refusing to self isolate for the two weeks and telling us it's all been blown out of proportion so they are having their holiday.
There are now cases of Covid in nearby Killarney and if rumour is correct the first one in our village.
So we'll all do what needs to be done to keep us safe and Dave will no doubt find another numbers conundrum with which to fascinate me.
If I'm not too glazed over I'll continue to make masks tucked away...far away in my sewing room.... :-)

[choux]

That is a shame, Gness. Stay safe.

[gness]

Thanks, Choux..... we'll try and you stay safe too....we all have a way to go yet....x