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TELEPHONE BOXHow much interest is lost on money sitting in phone boxes in England each year? Calculate for 2006 and 1985.

An swe rin g th is q u e stio n re q u ire s a n swe rin g a n u mb e r o f su b -q u e stio n s (SQ):

Question 1: How many telephone boxes are there in England?

Sta rt b y co n sid e rin g h o w ma n y p e o p le th e re a re p e r p h o n e b o x

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Th e re a re two te le p h o n e b o xe s in my villa g e a n d it h a s a ro u n d 2 0 0 h o u se s

Assu min g th a t th e a ve ra g e h o u se h o ld h a s fo u r p e o p le livin g in it (p a re n ts p lu s two ch ild re n ), th e n th e re a re : 2 0 0 h o u se s * 4 p e o p le / 2 b o xe s =4 0 0 p e o p le p e r p h o n e b o x in ru ra l a re a s

No w co n sid e r u rb a n a re a s, g ive n th e h ig h e r d e n sity o f h o u sin g , sa y d o u b le , th e re will b e 4 0 0 h o u se s p e r two p h o n e b o xe s

Ho we ve r, o ccu p a n cy ra te s a re like ly to b e lo we r in u rb a n a re a s e .g . mo re fla ts. Assu min g , th a t h a lf a re fa mily h o u se s with fo u r p e o p le a n d h a lf a re fla ts with two p e o p le , th e a ve ra g e h o u se h o ld will h a ve th re e p e o p le livin g in it

Th e re a re : 4 0 0 h o u se s * 3 p e o p le / 2 b o xe s = 6 0 0 p e o p le p e r p h o n e b o x in u rb a n a re a s

Fin a lly, a ssu me th a t in En g la n d 2 5 % o f th e p o p u la tio n live in ru ra l a re a s a n d 7 5 % live in u rb a n a re a s, th e n th e a ve ra g e n u mb e r o f p e o p le p e r p h o n e b o x is: 6 0 0 p e o p le * 7 5 % + 4 0 0 p e o p le * 2 5 % = 5 5 0 p e o p le p e r te le p h o n e b o x in En g la n d

Use th e p o p u la tio n o f En g la n d to e stima te th e n u mb e r o f b o xe s

To ta l n u mb e r o f p e o p le in En g la n d is ~5 0 millio n

To ta l n u mb e r o f te le p h o n e b o xe s is: 5 0 millio n / 5 5 0 p e o p le ~= 9 0 ,0 0 0

Question 2: How much money is in each phone box?

Un d e r th e a ssu mp tio n th a t te le p h o n e b o xe s will b e e mp tie d wh e n th e y a re fu ll a n d n o t b e fo re , we d o n o t n e e d to co n sid e r fre q u e n cy o f u se a n din ste a d re q u ire a n e stima te o f co in a g e ca p a city

Ph o n e ca lls co st 2 0 p in En g la n d so th e ma jo rity o f co in s will b e 2 0 p

Th e co lle ctio n tra ys in p h o n e b o xe s a re a p p ro xima te ly 2 0 cm h ig h , 2 0 cm wid e a n d 1 0 cm d e e p , g ivin g a to ta l vo lu me o f 2 0 * 2 0 * 1 0 = 4 ,0 0 0 cm3

A 2 0 p co in is a b o u t 2 cm in d ia me te r a n d a b o u t 1 /4 cm in d e p th , g ivin g a to ta l sp a ce ta ke n u p o f 2 * 2 * 1 /4 = 1 cm3

Th e re fo re , th e co lle ctio n tra y ca n h o ld 4 ,0 0 0 2 0 p p ie ce s wh e n fu ll, o r 8 0 0 th is a ssu me s th a t th e sh o o t in to th e tra y ma in ta in s a n o rd e rly co in

a rra n g e me n tAssu min g th a t th e re is a co n siste n t u se o f p h o n e b o xe s th ro u g h time , th e a ve ra g e a mo u n t in a p h o n e b o x is 4 0 0

Final Step: How much interest is lost on money sitting in phone boxes in England each year?

Th e a ve ra g e to ta l a mo u n t in a ll En g lish p h o n e b o xe s is: 4 0 0 * 9 0 ,0 0 0 = 3 6 millio n

Assu min g a n a n n u a l in te re st ra te o f 5 % o n d e p o site d mo n e y, th e to ta l a mo u n t o f in te re st lo st in a ye a r is 1 .8 millio n

Extra Question: Calculate for 1985.

Un d e r th e a ssu mp tio n th a t th e p h o n e b o x is e mp tie d wh e n it is fu ll, th e a ve ra g e n u mb e r o f co in s in th e b o x re ma in s a t 2 ,0 0 0

In 1 9 8 5 a ca ll co st 1 0 p ra th e r th a n 2 0 p so th e a ve ra g e a mo u n t in th e p h o n e b o x wa s 2 0 0 (ig n o re th e slig h tly d iffe re n t size s o f th e co in s)

We u se d to h a ve fo u r b o xe s in o u r villa g e in ste a d o f th e two we h a ve n o w Assu me th e re we re twice a s ma n y b o xe s in En g la n d in 1 9 8 5 i.e .

1 8 0 ,0 0 0 b o xe sTh e a ve ra g e to ta l a mo u n t in a ll En g lish p h o n e b o xe s wo u ld h a ve b e e n : 2 0 0 * 1 8 0 ,0 0 0 = 3 6 millio n

Assu min g a n a n n u a l in te re st ra te o f a b o u t 1 0 % in 1 9 8 5 , th e to ta l a mo u n t o f in te re st lo st in a ye a r wa s 3 .6 millio n

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