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Annual Compound Interest - Fraction of a year

tbsgadi
tbsgadi asked
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Last Modified: 2012-05-06
What is the accepted way (For accountants?) to calculate Annual Compound Interest when you have a fraction of a year. eg 9.5 years.
(1+i)^9.5
(1+i)^9
(1+i)^9 *(1+i/2)

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tbsgadi,

=((B2/A2)^(1/9.5))-1

It's in the attached file

Hope it helps

Patrick

tbsgadi-01.xls

Author

Commented:
I know how to calculate compound interest.

My question is whether the acceptable practice, is to compound fractions of years where in reality if it is annualy compounded, the extra interest from a fraction of a year wouldn't be received.
ozo
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Most Valuable Expert 2014
Top Expert 2015
Commented:
any of them could be justified mathematically,
in financial situations, whoever sets the terms might want to chose the one that as as financially advantageous to them as they can get away with.
when you have computers to track interest, there seems little reason to have a compounding period as long a year, so the third option was probably adopted for simplicity of calculation.
There may also be particular accounting rules about how to handle rounding.

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>What is the accepted way (For accountants?) to calculate Annual Compound Interest when you have a fraction of a year. eg 9.5 years.

There is no accepted way as interest is given or charged at whatever rate and method is agreed upon between the interested parties.

Author

Commented:
You're saying that if I go to 3 different banks & ask for a bank statement each will calculate differently?
deightonprog

Commented:
when I worked in this sort of thing, the standard was to pay the interest based on simple arithmetic fractions

so if the interest is calculated at the end of the year and you had 100,000 in for the first half year or so and then it dropped to 50,000 you might get at 10% interest

100,000 * 180/365 * 0.1 + 50000 * 185/365 * 0.1

so you might have thought that the interest on the 100,000 should be getting interest in the second half of the year, but it wasn't!

Some banks spotted this potential stinginess and as a marketing feature started offering 'daily interest' accounts   where interest is calculated per day and then compounded daily.  it gives some advantage to the saver, but this might be marginal, however that extra cost to the bank means their headline rate might be a little bit lower and in marketing terms it can make a difference.  So I offer you 4.25% daily interest and someone else says 4.3% using the simple method, many people would just think 4.3 v 4.25 - no brainer.

there's something called the 'AER' in the uk, I think reflects these differences in calculations.
AER in the UK is defined as in this link:

http://www.investopedia.com/terms/a/aer.asp

However that has little to do with what is offered by different institutions nor how they calculate interest as the method they used is specific to a particular account.
ozo
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Most Valuable Expert 2014
Top Expert 2015

Commented:
patrickab is saying that each may calculate differently if it so chooses.
in practice there are often differences in interest rates, when deposits to clear, penaltys for early withdrawl, day of the month when payment is due, etc.
but I would not expect many banks out of 3 to compound yearly, unless your statement involves enough money that the bank would want to let you participate in setting  the terms.
>You're saying that if I go to 3 different banks & ask for a bank statement each will calculate differently?

Yep, that's how it works here in the UK. In fact there are dozens of different methods offered. Declaring the AER is meant make them easily compared and to an extent that applies but only to a certain extent.

Author

Commented:
I'm building a program for the Private Equity World, that amongst many other things, calculates interest on loans/Shares etc.
I give the user the option to choose which kind of interest calculation ...Simple -compound monthly ,compound quarterly etc.
I give the Loan Issue date & want to calculate the accumulated amount for today's date. Hence my question.
In the UK it gets even worse as only some accounts offer fixed rates of interest. Most financial institutions in the UK offer new savers a decent rate for a fixed term say a year, and then drop the rate sharply after that initial period. However they still offer new savers better rates than longer term savers. So what looks good to start with is usually only good for a year. After that you will need to move your money to a different institution and open a new account at a better rate. Most institutions assume that the average saver can't be bothered to move their money after a year with the result they attract new customers at the expense of their existing customers.

So all the carefully calculated interest rates become pretty worthless if one is not prepared to move your money regularly - every year without fail if you want the best rate ruling at that time.

Author

Commented:
For my purpose I'm only dealing with fixed interest.
There is no easy answer to your question. The reason is that there are too many methods used to be able to just offer an option of say 4 or 5 different methods. As soon as you get into interest/values of financial intruments then you are entering a complex area. We have lots of accounts and they almost all operate different interest rate schemes. Most of the problems revolve around the first and subsequent year interest rates, the penalties for withdrawing, the frequency of adding interest, whether we choose to have interest paid into a different accounts and so on.
>For my purpose I'm only dealing with fixed interest.

Then find out from the institutions that are relevant to your application how they calculate interest. It's specific questions to specific organisations. No amount of pontificating by us will help you. You need to contact the organisations and ask the questions yourself.

Author

Commented:
if Anybody is intersted in the different possibilities have a look at this
http://www.swx.com/download/trading/products/bonds/calculator.xls
tbsgadi - Thanks for the grade - Patrick
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