How interest is calculated on fixed term deposit account.

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Sue Ellen

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There is not a large amount of money involved here but I am just intrigued as to how the figures are arrived at in the calculation of the interest on my fixed term deposit account.

I opened the account this year and this is how the figures stack up since then

25/6 3.50% €23.78 10,023.78
25/7 3.55% €23.40 10,047.18
25/8 3.55% €25.80 10,072.98
25/9 3.58% €24.30 10,097.28

The interest is at the standard rate. What I need to understand is why if the interest rate goes up slightly and the initial investment has increased why does the interest earned go down? Just want to get my head around this for future reference.
 
I assume interest is calculated daily, so it's probably due to the variable number of days in each monthly interest period, e.g.

May/June 31 days
June/July 30 days (so smaller)
July/Aug 31 days (so largest so far)

I can't explain why Aug/Sep is less (paid on 25th Sep, so less days in September shouldn't be relevant.).

Do the T&Cs state what the interest period is?
 
Here is the answer and Formula and your forecast for October

............Capital Rate% Days Gross Dirt Net New Capital
May-Jun 10000.00 3.50 31 29.73 5.95 23.78 10023.78
Jun -Jul 10023.78 3.55 30 29.25 5.85 23.40 10047.18
Jul- Aug 10047.18 3.75 31 32.00 6.40 25.60 10072.78
Aug-Sep 10072.78 3.58 31 30.63 6.13 24.50 10097.28
Sep-Oct 10097.28 3.58 30 29.71 5.94 23.77 10121.05

I think you must have mistyped the August Interest - It calculates out at 3.75% !

Please pm me and I will send you the spreadsheet
 
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From this 2001 thread

The APR concept is relatively simple. Start with the basics: an APR of 10% means if I borrow £100, I repay exactly £110 exactly one year later. Thats why they call it ANNUAL PERCENTAGE RATE!

Now lets look at rates over other periods. Suppose I have a £100 overdraft at the start of year at an APR of 10%. In theory, if I make no other transactions on the a/c (inc fees charges etc.) I should owe exactly £110 at years end. How is this done if interest is charged, say, quarterly? Well, its not simply a question of paying 2.5% interest per quarter. Why? Because in quarter 2 I'd end up paying interest on £100 + £2.50 (total interest for the quarter being £2.5625, in quarter 3 I pay interest on £100 +£2.5625 + £2.50 etc.

To get the true quarterly rate I must convert the interest rate to the format 1+i where i is the decimal equivalent of the APR. In this case APR =10% = 0.1 so my 1+i format = 1.1 (which is the number I must multiply the year start debt by to get the year end debt.) Then get the fourth root of 1.1 (or the square root of the square root of 1.1) to get the 1+i factor for one fourth of a year. This is 1.024113589.... Therefore the true interest rate per quarter is 2.4113689%

You can check this as follows:
Quarter Opening balance Interest Closing Balance
1 100 2.411359 102.411359
2 102.411359 2.469505 104.880864
3 104.880864 2.529054 107.409918
4 107.409918 2.590039 109.999957

Correct apart from rounding errors; all figures shown to 6 decimal places.


Similarly the true daily rate is (the 365th root of 1+i) -1
In this case this is (the 365th root of 1.1) - 1
= 1.000261158 - 1
= .000261158
= .0261158% per day.

The Excel formula for 365th root of 1.1 is =1.1^(1/365)


Lesson 2 is how to calculate the APR when you know the repayments. Thats for honours students!
 
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