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I recently requested a statement from SF England regarding my student loan outstanding debt. Once I had this I was leafing through but started to become confused about their methods of calculating compound interest.

If you consider the opening transaction and the interest calculation:

Opening transaction and interest calculation

You observe that in the first months interest calculation (I've omitted the exact dates for security), with an interest rate of 6.3%, a figure of £5.35 from an initial total of £1179.75. Obviously 6.3% of the initial value is not 5.35.

Presuming that there might have been some hidden fees or slight deviance given that it was the first month I began to look into later months to see if the same trend continued:

Again the same mismatch can be observed

I am reasonably certain I have the definition of compounding interest to be correct. Taken from the definition here: https://www.thecalculatorsite.com/articles/finance/what-is-compound-interest.php

The examples I have shown do not have any repayments on the outstanding so I would have thought the calculation would have been simple, the interest rate of that month applied to the running total and then added together for next months running total. I have attempted to contact SFE on this matter but have achieved nothing.

Is there anything that I have omitted from my own calculations or gaps in my knowledge? Or perhaps anyone can shed some light on what might be happening.

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As far as I can tell (more info here https://www.gov.uk/guidance/how-interest-is-calculated-plan-2 ) interest on Plan 2 student loans is calculated daily and compounded monthly.

This means on Day 1 they calculate 1/365 of the annual interest rate on the amount you currently owe. Remember this number, but don't do anything else with it yet.
On Day 2 they do the same calculation, get the same answer.
On Day 3, 4, 5, 6.... repeat.
On Day 30, do the same calculation. Now add up the answers that you remembered from the calculations you have done and add that to the loan balance.
New month starts now.
On Day 31, do the same calculation (but now the "amount you currently owe" is different from what it was on the previous 30 days).
On Day 32... repeat
On Day 61 (last day of the month), do the same calculation. Again add up the answers that you remembered from the calculations you have done this month and add that to the loan balance.

In other words, you can multiply the interest rate by 30/365 (or however many days there are in the month) and then multiply the answer by the starting balance for the month.

In the later examples you gave this works out. In the first example it looks like it was a 26 or 27 day month - which might imply the loan started on the 3rd or 4th of the month and they then calculate it on the calendar month ends after that?

Edited to address questions from comments:

Another source I was using suggested much the same methodology that you detail, with the exception of multiplying the interest by (Days)/36500. Using that instead of dividing by 365, seems to give a result in the right ball park (though I could not tell you why).

6.3 is a percentage interest rate, so when you are using it in a calculation you need to use 0.063 as a multiplier rather than 6.3. You get the same effect by dividing 6.3/36500 or 0.063/365.

The formula for my later example would derive to: (6.3*(30/36500))*12857.21 = 66.58 This doesn't quite match up to the 66.88 offered by their calculations but either there is a deeper time calculation of days done by their system or our methodology is incorrect.

By the time you're within 30p of their calculation my advice is to stop worrying about it. They might be using 366 days in the year, or 365.25, and the days in the month might be 30 or 365/12 or 365.25/12 or... etc.

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  • It appears we are getting closer to an answer, and for that many thanks. Couple of caveats though, I think. Another source I was using suggested much the same methodology that you detail, with the exception of multiplying the interest by (Days)/36500. Using that instead of dividing by 365, seems to give a result in the right ball park (though I could not tell you why). Further assumptions I have made involve removing a day in the day range to take into account for error in time of calculation and so forth.
    – Sisha
    Feb 24 at 14:30
  • Given the above. The formula for my later example would derive to: (6.3*(30/36500))*12857.21 = 66.58 This doesn't quite match up to the 66.88 offered by their calculations but either there is a deeper time calculation of days done by their system or our methodology is incorrect.
    – Sisha
    Feb 24 at 14:31
  • @Sisha I've edited my answer to address your comment.
    – Vicky
    Feb 24 at 16:04
  • Perfect, many thanks
    – Sisha
    Feb 24 at 16:06
  • @Sisha 66.88 is 12857.21 * 1.063^(31/365) - 12857.21
    – fgb
    Feb 24 at 16:40

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