Financial matters

[devonwoody]

Trawling through my portable harddrive (which members here have be kind enough to assist me this week, I found this little treasure:

Another useful rule of thumb is the "Rule of 72". This states that if you divide a rate of interest into 72, the resulting number is the number of years for your capital to double if that interest is compounded.

So, for example, if you apply 6% to your capital (reinvesting the interest) then it will take 12 years to double your money. Try applying 6% to £100 for 12 years. Your calculator will show a final answer of £201.22 - so it's a pretty good approximation - huh?!

Alternatively, using the same rule, with inflation of 3% it will take 24 years for your capital to halve in its buying power. The actual answer is a smidgeon (this is a technical term) under 23 years, so the rule works pretty well.

OK - sorry - but I find this stuff interesting anyway. I'm a sad man, I know. I'll get me coat!

 

[Random Orbital Bob]

Fascinating DW. If only there were some decent interest rates around to bother applying your excellent rule to

 

[bugbear]

Fascinating DW. If only there were some decent interest rates around to bother applying your excellent rule to

Wonga (and their friends) have some enormous rates to have arithmetic fun with!

BugBear

 

[Random Orbital Bob]

Yes BB I was rather thinking of making money , not losing my shirt

 

[devonwoody]

Fascinating DW. If only there were some decent interest rates around to bother applying your excellent rule to

Yes I think it was around 2001 I downloaded that from somewhere, I think I still had some 10% bonds coming towards maturity.

 

[doctor Bob]

Anyone see Japan now has an interest rate of -0.1%, first time a negative rate has existed i believe. It's to encourage business to invest rather than save, in the hope it kick starts their economy.

 

[Myfordman]

Peer to Peer lending can get you some good rates of return Bob.
There is an element of risk but you can spread that over a number of loans.
Gross rates of 10-13% are out there secured against assets. 12% is common.

As an example, keep 80% of your cash in 1% bsoc/bank safe accounts and 20% in P2P at 12% will get an average rate of 3.2% gross

That is 22.5 years to double compared to 72 years with all at 1% using the DW rule.

 

[Student]

I used to be able to prove DW's rule (using logarithms). When I learned the tip, interest rates were about 3%* pa and the magic number was 70. However, once you go above 5%, 72 gives a more accurate answer.

Another mathematical conundrum: how many people do you have to have in a room for there to be a better than even chance that two will share the same birthday (day and month, not year)?

* A few years later they hit 15%!

 

[devonwoody]

Student, I was at passport control once London A., and the desk lady said "you have the same birthdate as me.

What odds? :roll:

 

[Myfordman]

I've just a few sums on the accuracy of the formula and the results are in the attached chart.


Read along the accuracy ratio =1 line and compare the interest rate to where the lines cross and read off the constant to use.

So 72 is about right of 8% interest whereas using 70 is nearer for 2%
If we ever get to the giddy heights of 14%, then use 74.

The correct formula for the number of years to double your money is given by

N (years) = log(2)/log (1+i/100) where i= percentage interest rate.

 

[marcros]

Student, I was at passport control once London A., and the desk lady said "you have the same birthdate as me.

What odds? :roll:

1 in 365

 

[Phil Pascoe]

I seem to remember 23 to 1. It didn't make much sense to me though.

 

[Bm101]

1 in 365 for birthdays, for birthdates including years it would be .... more than my tiny brain could... wait....I think I have it.... I can feel the regular rhythm of my brain when it starts working at peak efficiency! *drip drip drip.
Ah no, it seems my ears have just stared bleeding.

 

[marcros]

in my mind, dw's birthday could have been any day at all, and the question was actually what are the odds of the lady at the counter having a birthday on a particular day.

if it were what are the chances of 2 people having the same birthday, it would have been 1/365 x 1/365

when it comes to people in a room, it gets interesting. I forget the maths of it, but i do remember the answer being much less than you would expect.

 

[Cordy]

Student, I was at passport control once London A., and the desk lady said "you have the same birthdate as me.

What odds? :roll:

When I went for a blood test; routine check-up, the practice nurse said 'We have the same birthday'

What odds she says that to most of her patients ? #-o

My major shares investment is Debenhams , going OK and pay a decent dividend

No advice intended

 

[doctor Bob]

in my mind, dw's birthday could have been any day at all, and the question was actually what are the odds of the lady at the counter having a birthday on a particular day.

if it were what are the chances of 2 people having the same birthday, it would have been 1/365 x 1/365

when it comes to people in a room, it gets interesting. I forget the maths of it, but i do remember the answer being much less than you would expect.

Forget the maths professor, Stick to woodwork ............. :lol:

 

[Bm101]

While there's mathematicians about, I just filed my tax return. Looking in a little more detail at a PAYE coding notice I noticed that HMRC had estimated my average earning for this year at £100 000. Really.
After buying a yacht and a provisioning some contacts for a 'working holiday' to Bolivia, I came back down to reality. Bearing in mind I work for a company that employs 40 000 odd people world wide, and they have messed my tax codes up more than once, and, that the explanation for paying super tax on my wages for a year from HMRC was 'oooh i don't know. It looks like a computer error!' Oh really.
So, mathematicians!
What's the mathematical possibility i get an apology off anyone?

 

[Bm101]

Also Marcros, What about Leap Years! :shock:

 

[Phil Pascoe]

Yes, it was 23 people in a room to get two with the same birthday I was thinking of.

 

[Student]

23 is the answer although, to my shame, I had to look up the maths. My excuse is that I did my probability and statisti8cs exam, and compound interest exam for that matter, 45 years ago. I don't know whether Myfordman did his calculations on a spreadsheet or managed to download it from somewhere; either way, my thanks for showing the answer. When I studied did compound interest, we had to use logs and/or slide rules and to complete that graph would have taken quite a time.

Going back to birthdays, the chance of having the same birthday as another person, as mentioned previously, is 1/365.

Consequently, the chance of 2 people having different birthdays is:

1-1/365 = 364/365 = 0.99726

However, with 23 people we have 253 pairs of people:

(23 x 22)/2 = 253

Having all 253 pairs different is like getting heads 253 times in a row (let’s assume birthdays are independent). The probability is then:

(364/365) ^ 253 = 0.4995

Although 99.7260% is really close to one, when you multiply it by itself a few hundred times, it shrinks; fast. So the chance that all 23 have different birthdays is 49.95% and the chance that we have a match is: 1 – 49.95% = 50.05% i.e. better than even,

For 73 people, the chance of a match is 99.9%.

In DW’s case, the lady at passport control probably sees hundreds of people in a day so she is quite likely to find a match sooner of later.

Off to get an ice pack!