# Historical Calculations how were they done



## RichInSpirit (29 Aug 2017)

It was just running through my mind yesterday about how did they (banks and the like)  work out stuff like compound interest for loans, deposits , investments long ago in a time before calculators and computers.
Say for compound interest for 20 years did they have to multiply it all out year by year ? On paper. It must have been terrible time consuming.

Any historical bankers out there ?


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## Monbretia (29 Aug 2017)

I don't know how far back you are thinking, I started in the bank in 1979 and we had a computer, mind you it was the size of a small car!


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## dub_nerd (29 Aug 2017)

I remember having a post office account as a small kid, very early 70s. If I remember right you had to post your account book to somewhere and it came back with the interest written in by hand. No idea how they calculated it though.


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## Brendan Burgess (29 Aug 2017)

RichInSpirit said:


> Say for compound interest for 20 years did they have to multiply it all out year by year ? On paper. It must have been terrible time consuming.



That is exactly what they did. On savings accounts, you would see it in the book. 

Mortgage interest was calculated on the "annual rest" basis, so it was much easier. You paid interest on the balance outstanding at the start of the year.  Normal repayments did not affect the calculations.   Additional repayments required a refund of interest. 

Brendan


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## newirishman (29 Aug 2017)

What was used was pre-calculated (and printed) interest tables, with various scenarios, and eventually a lot of manual calculations.
Despite what one might think, the maths for interest calculations etc. is not that complicated or onerous. Of course, a spreadsheet and excel makes life much easier and of course quicker, but there money and moneylending was around long before mechanical or electronic calculators.
But it is pretty much straightforward to do up some tables with various scenarios, enough in any case to get an good enough idea on repayment figures.

EDIT: it is onerous and time consuming compared to using computers. And banks used to have "a lot" of people doing sums. But things were different of course 150 years ago


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## dub_nerd (30 Aug 2017)

I suppose the trick answer could be "there have always been computers". When the word was coined nearly five hundred years ago, a computer was a person. (The first usage relating to a calculating machine dates from 1897). A thousand years before the invention of the word you could point to the invention of the decimal system and the placeholder digit zero in India in the 7th century, its adoption by the Persians and Arabs in the 9th century, and in Europe in the 10th. Also borrowed from India, along with these came the use of negative numbers to represent debts in book keeping. The Chinese were using negative numbers even earlier, in the 2nd century and probably earlier still.


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## PMU (30 Aug 2017)

newirishman said:


> What was used was pre-calculated (and printed) interest tables, with various scenarios, and eventually a lot of manual calculations.


 A copy of "Brayshaw's Mathematical Companion" would help you in the pre-calculation and also how to do things like 'calculate the cost per bushel when the price per quarter is given', etc.  (I've no idea what that actually means.)


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## Black Sheep (31 Aug 2017)

Dub nerd, Have you still got that little Post Office book with your first communion money in it. Perhaps that's my writing there.  Yes indeed it was worked out manually on the scribble pad and written in to the books, very labour intensive indeed and we were also paid buttons for it.


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## losttheplot (31 Aug 2017)

I still have one of the light brown post office books. Opened in 1982. Has £8 in it (plus interest). I'm sure they'd laugh at me if I went into the post office with it.


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## RichInSpirit (1 Sep 2017)

Thanks everyone for your informative answers. Interesting that interest was worked out on paper. I suppose interest didn't really have to be calculated more than a year at a time so even compound interest is just simple interest for the year.


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## dub_nerd (1 Sep 2017)

losttheplot said:


> I still have one of the light brown post office books. Opened in 1982. Has £8 in it (plus interest). I'm sure they'd laugh at me if I went into the post office with it.



Mine was one of those light brown ones too, but from ten years earlier. I remember it fondly, but I don't still have it unfortunately. I probably withdrew all the money to fund the necessities of life (e.g. Tayto crisps which went from 6d -> 2½p at decimalisation, and silvermints 5d -> 2p).


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## RichInSpirit (1 Sep 2017)

A Google search brought up slide rules which are probably like mini computers. They look complicated but i'm sure if you learned how to use them they would be simple. But still not as handy as calculators or computers.
For calculations with powers in them logarithms can simplify multiplication and division down to adding and subtraction.
But logarithm s themselves look very complicated.


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## dub_nerd (1 Sep 2017)

RichInSpirit said:


> A Google search brought up slide rules which are probably like mini computers. They look complicated but i'm sure if you learned how to use them they would be simple. But still not as handy as calculators or computers.



Somebody gave me a birthday present of a slide rule when I was a kid, so I know how to use one. Affordable pocket calculators had already appeared so a slide rule wasn't of much _practical _use. I think the well-intended idea was that knowing how a slide rule worked was good maths training. I also remember using a book of log tables at school which presumably disappeared soon after.

I don't think a slide rule would be much good for financial calculations where you have to guarantee precision to the nearest cent. They are more of a scientific instrument where precision to a certain number of significant digits is of use. With money calculations the number of decimal places precision would reduce with the size of the amount involved.



RichInSpirit said:


> For calculations with powers in them logarithms can simplify multiplication and division down to adding and subtraction.
> But logarithm s themselves look very complicated.



Slight correction -- logs reduce calculations with powers down to multiplication/division and reduce multiplications/divisions to addition/subtraction. The basic concept of using logs for calculation is not all that complicated. You implicitly work with the exponent of the base of your logs and rely on the properties of exponentiation:


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## Duke of Marmalade (1 Sep 2017)

Prior to 1971 we didn't have a decimal currency.  Even modern spreadsheets would struggle with that

In my first job in an actuarial office we had these lumpy calculators* (the type accountants still use today).  They could add and subtract multiply and divide but they couldn't raise to a power, crucial for compound interest calcs.  We became dab hands at devising algorithms to achieve this end which depended much more on digital dexterity in use of the machine than any intellectual effort.  We used to time ourselves and set records for the fastest calc of say the present value of 12 monthly installments.

*  the type where if you keyed in 71077345 and looked at it upside down you saw "SHELL OIL".


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## dub_nerd (2 Sep 2017)

Some fascinating anecdotes on this thread, thanks folks.


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