# Interest on Term Deposit accounts



## tom82 (7 May 2014)

How do banks calculate interest on term deposits, what is the formula for this?
What I thought was the calculation didn't seem to equal what the bank calculator on website said so want to know how to calculate it myself.
Thank you


----------



## pixel (7 May 2014)

tom82 said:


> How do banks calculate interest on term deposits, what is the formula for this?
> What I thought was the calculation didn't seem to equal what the bank calculator on website said so want to know how to calculate it myself.
> Thank you




Like everything else, the term deposit rates are determined by supply and demand.
If a Bank has a particular investment project, for which $xxx is needed short-term, they may offer a premium to the RBA cash rate. For other terms they may simply leave the rate at RBA cash and bank the difference (to, for example, business loans or mortgages) as their profit.
On a site such as http://www.ratecity.com.au/term-deposits/ you will notice some small differences. Whenever I find a TD mature and ready to be rolled over, I don't check any hypothetical calculators, but simply check Ratecity or the banks' website; then I'll pick the best current offer and term.

Not unlike Coles and Woolworths really: One may sell today's bananas a few cents cheaper, next week it's the other way around. But you won't find any rhyme or reason WHY.

Once you've settled on a term and amount, the calculation is simple: Most banks will use the formula "Principal times daily interest rate times number of days". Differences between their and your calculation should only occur after the decimal point. If memory serves me correctly, Banks use 360 days per year; the number of decimals they apply in their algorithm and the direction they round up or down may also differ from yours. And that would give slightly different results. Hardly worth arguing about - unless you do find a discrepancy significant enough to ask ... :1zhelp:


----------



## tom82 (7 May 2014)

pixel said:


> Like everything else, the term deposit rates are determined by supply and demand.
> If a Bank has a particular investment project, for which $xxx is needed short-term, they may offer a premium to the RBA cash rate. For other terms they may simply leave the rate at RBA cash and bank the difference (to, for example, business loans or mortgages) as their profit.
> On a site such as http://www.ratecity.com.au/term-deposits/ you will notice some small differences. Whenever I find a TD mature and ready to be rolled over, I don't check any hypothetical calculators, but simply check Ratecity or the banks' website; then I'll pick the best current offer and term.
> 
> Not unlike Coles and Woolworths really: One may sell today's bananas a few cents cheaper, next week it's the other way around. But you won't find any rhyme or reason WHY.




I'm not sure you understood the question. Lets see if I can word it a different way.
What is the formula used to calculate interest on a term deposit account?

Thank you


----------



## pixel (7 May 2014)

tom82 said:


> I'm not sure you understood the question. Lets see if I can word it a different way.
> What is the formula used to calculate interest on a term deposit account?
> 
> Thank you




sorry Tom, 

I accidentally sent the first part off before I had completed the reply


----------



## tom82 (8 May 2014)

pixel said:


> sorry Tom,
> 
> I accidentally sent the first part off before I had completed the reply




Ok, no worries, what was the second part?


----------



## DJG (8 May 2014)

tom82 said:


> I'm not sure you understood the question. Lets see if I can word it a different way.
> What is the formula used to calculate interest on a term deposit account?
> 
> Thank you




Do you want simple or compound interest?


----------



## tom82 (8 May 2014)

DJG said:


> Do you want simple or compound interest?




Which do banks use?

How about both?
Both would be good to know.

Thanks


----------



## McLovin (8 May 2014)

tom82 said:


> Which do banks use?
> 
> How about both?
> Both would be good to know.
> ...




They use compound interest. It's usually calculated daily and paid (compounded) monthly/quarterly.

Here's the formula:

https://qrc.depaul.edu/StudyGuide2009/Notes/Savings Accounts/Compound Interest.htm


----------



## tom82 (8 May 2014)

McLovin said:


> They use compound interest. It's usually calculated daily and paid (compounded) monthly/quarterly.
> 
> Here's the formula:
> 
> https://qrc.depaul.edu/StudyGuide2009/Notes/Savings Accounts/Compound Interest.htm




Ok, thank you.

So to clarify, the formula is?

A = P * (1 + r/n) * n * t

Where / how do you find out how often they calculate the interest, haven't seen anything on bank sites stating how often they do that?


----------



## McLovin (8 May 2014)

tom82 said:


> Ok, thank you.
> 
> So to clarify, the formula is?
> 
> ...




No it's ^nt.

All the info should be in the t&c's, product disclosure statement etc.


----------



## tom82 (8 May 2014)

McLovin said:


> No it's ^nt.
> 
> All the info should be in the t&c's, product disclosure statement etc.




^ ?


----------



## McLovin (8 May 2014)

tom82 said:


> ^ ?




To the power of.


----------



## tom82 (22 May 2014)

McLovin said:


> To the power of.




Thanks for the reply.

To help me understand this better would you be able to show me an example of how to do this calculation?

Thanks


----------



## McLovin (22 May 2014)

tom82 said:


> Thanks for the reply.
> 
> To help me understand this better would you be able to show me an example of how to do this calculation?
> 
> Thanks




Sure

For simplicity's sake assume interest is paid annually.

Interest rate (r) = 10%
Time (t) = 5 years
Principal (P) = $100

A=P(1+r)^t
A= $100(1+0.1)^5
A= $161.051

If interest was being paid quarterly then you'd adjust...

Interest rate (r) = 10%
Time (t) = 5 years
Principal (P) = $100
Number of compounding periods/year (n) = 4

A=P(1+(r/n))^nt
A=$100(1+(0.1/4))^4*5
A= $163.86


----------



## tom82 (22 May 2014)

McLovin said:


> Sure
> 
> For simplicity's sake assume interest is paid annually.
> 
> ...




I did the calculation and got 1.61051.

If the time was less than a year say 90 days or 180 or some such would you replace 5 with the number of days?
Do you need to tell the calculation how often the interest is calculated in the time?


----------



## McLovin (22 May 2014)

tom82 said:


> I did the calculation and got 1.61051.




Multiply by $100



tom82 said:


> If the time was less than a year say 90 days or 180 or some such would you replace 5 with the number of days?
> Do you need to tell the calculation how often the interest is calculated in the time?




No. The exponential (ie the ^nt) bit is the number of times in total over the period that your money compounds. Basically, the interest rate needs to match the compounding period. So if you're compounding twice/year then (i) becomes 5%/period and the periods go from 5 to 10. See my second example above...


----------



## tom82 (22 May 2014)

McLovin said:


> Multiply by $100
> 
> 
> 
> No. The exponential (ie the ^nt) bit is the number of times in total over the period that your money compounds. Basically, the interest rate needs to match the compounding period. So if you're compounding twice/year then (i) becomes 5%/period and the periods go from 5 to 10. See my second example above...




So if a bank says they calculate the interest every day of the term do mean they are compounding it everyday, is it the same thing?


----------



## tom82 (22 May 2014)

That second example I got 5.51.


----------



## McLovin (22 May 2014)

tom82 said:


> So if a bank says they calculate the interest every day of the term do mean they are compounding it everyday, is it the same thing?




It means if you put money in, it will start earning interest that day. But the bank will only pay interest monthly or quarterly. And compounding in this sense means earning interest on interest. I suppose you could knock up a spreadsheet that will do it all for you otherwise it's going to be very tedious, especially if you have a lot of txns going through.


----------



## tom82 (22 May 2014)

McLovin said:


> It means if you put money in, it will start earning interest that day. But the bank will only pay interest monthly or quarterly. And compounding in this sense means earning interest on interest. I suppose you could knock up a spreadsheet that will do it all for you otherwise it's going to be very tedious, especially if you have a lot of txns going through.




Ok, I get that if you put money in it starts earning interest the same day. Yes, I have seen monthly, quarterly and at maturity.
So does that mean they only compound on the day they pay the interest?


----------



## tom82 (22 May 2014)

Is there a book that contains useful formula to calculate these sorts of problems?


----------



## McLovin (22 May 2014)

tom82]That second example I got 5.51. [/QUOTE]

You got to use brackets or simplify it before you plug it into the calculator..

Try

A=$100(1+(.025))^20

Or even 

$100(1.025)^20

[QUOTE=tom82 said:


> So does that mean they only compound on the day they pay the interest?




Yeah, otherwise you'd be earning interest on interest that hasn't been paid to you.


----------



## tom82 (22 May 2014)

McLovin said:


> You got to use brackets or simplify it before you plug it into the calculator..
> 
> Try
> 
> ...




Yes i did use brackets. This time I got 1.63 and * 100 for 163.86.

If the number of  periods in the year it was being compounded was 4, where do you get 20 from?


----------



## McLovin (22 May 2014)

tom82 said:


> Yes i did use brackets. This time I got 1.63 and * 100 for 163.86.




If you enter the forumla correctly you'll get 163. [hint it's the first part of the equation!]



tom82 said:


> If the number of  periods in the year it was being compounded was 4, where do you get 20 from?




Because it compounds 4x/year for 5 years...4*5=20


----------



## tom82 (22 May 2014)

So how many compounding periods are when the term is less than a year?
1?

Lets say one has $10 000, interest of 3.15% for 180 days.

Interest rate = 3.15%
period of time= 180 days
Principal = 10 000


----------



## McLovin (22 May 2014)

tom82 said:


> So how many compounding periods are when the term is less than a year?
> 1?
> 
> Lets say one has $10 000, interest of 3.15% for 180 days.
> ...




Well you have the interest rate, all you need is to know how often the bank pays the interest.

If it's monthly then the monthly interest rate is .002625, and if it's in there for 180 days that's six months, so six compounding periods.


----------



## tom82 (22 May 2014)

McLovin said:


> Well you have the interest rate, all you need is to know how often the bank pays the interest.
> 
> If it's monthly then the monthly interest rate is .002625, and if it's in there for 180 days that's six months, so six compounding periods.




Where and how do you get the 0.002625?


----------



## McLovin (22 May 2014)

tom82 said:


> Where and how do you get the 0.002625?




Come on dude this isn't rocket science.

.0315/12...


----------



## tom82 (22 May 2014)

tom82 said:


> So how many compounding periods are when the term is less than a year?
> 1?
> 
> Lets say one has $10 000, interest of 3.15% for 180 days.
> ...




But one has to know when and how to convert amounts from the total percentage to a monthly percentage.
If one has all the information to begin with it would be straight forward to calculate but even that website that was linked to does not go into enough detail, not all the steps are shown. If one doesn't know they have to break something down further how can they get the correct answer. If all the steps were shown clearly it would help.

I do appreciate your time and assistance with this!

Interest rate = 3.15% becomes 0.0315 / 12 = 0.002625
period of time= 180 days
Principal = 10 00

x=10 000(1+0.002625)^6
x=1.0158537218457713417591896057129 * 100
x= 101.58

Not sure that looks right.


----------

