Money Puzzler

[888]

If I save a penny on 1st January, 2p on the 2nd Jan, 3p on the 3rd etc. how much is already saved up to today?

[Mamyalynne]

http://www.ohsoamelia.com/2016/01/365-day-money-saving-challenge-free.html

[888]

Thank you for this, I wondered if anyone was doing it and how much was totalled up so far.

[JJ109]

Up to today 87 days have passed since 1st january(31 +28 +28)
Therefore you have a sequence to add
1+2+3+4....+85 +86 +87
to do this add
1 + 87 = 88
2 + 86 = 88
3 + 85 = 88
and so on
There are 87/2 = 43.5 pairs of numbers that all add to 88p
Therefore sum saved to date= 43.5 x 88p = 38.28 pounds

[888]

Thank you Jj, so tomorrow is £38.29 and so on? Didn't think it was so much so soon. End of December will be interesting!

[JJ109]

No - tomorrow will be 38.28 + 88 = 39.16. The day after will be 39.16 + 89 = 40.05

[JJ109]

The formula is (1 + n) x (n/2) where n is the number of days
100 days savings = (1+100) x (100/2) = 101 x 50 = 50.50 pounds
200 days savings = (1 + 200) x (200/2) = 201 x 100 = 201.00 pounds
300 days savings = (1 + 300) x (300/2) = 301 x 150 = 451.50 pounds
etc etc

[Mexican18]

Well done,JJ!

[888]

Yes Jj! And that's a thank you from me too.