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Posted on 2009-02-19

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)

Thanks

(1+i)^9.5

(1+i)^9

(1+i)^9 *(1+i/2)

Thanks

16 Comments

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.

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.

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

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.

http://www.investopedia.co

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.

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.

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.

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.

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.

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.

http://www.swx.com/downloa

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