Self assessment - credit balance

[Jupiter01]

It’s one of those rare occurrences where I am owed money by HMRC upon the completion of my self assessment. I did insert my bank details into the self assessment for any credit that may be due.

How long does it typically take before this money is in my bank account and is there anything else I need to do?

Thanks in advance.

[Jholm]

Generally 2-4 weeks. However, there doesn't seem to be much rhyme or reason, with some getting in days and some taking months and months.

[Jupiter01]

Thanks. Is there anything else I need to do? As stated earlier, I’ve put my account details in the tax return.

[Jholm]

You shouldn't need to but might want to log into SA and request the repayment, once the balance shows as a credit.

I assume this repayment is all those pension contributions paying off!

[Jupiter01]

Oh yeh, pension tax relief
I went in and as you suggest, I had to claim the tax refund and as part of this, insert my bank details again.it then said that the payment wil be made within 2 days and can take up to 4 weeks. Bizzare as I had specified this as part of my tax return….

I will now put this money back into the pension and on and on goes this cycle. In reality, the tax relief is way more than what we are led to believe once you start to reinvest the original tax relief amount. Am I understanding this correctly?

[someone]

In reality, the tax relief is way more than what we are led to believe once you start to reinvest the original tax relief amount. Am I understanding this correctly?

It depends on how you do the sums.

Scenario 1:

I know I'll have 20K to invest into my pension once all the tax relief is sorted. In order to get 20K into my pension I need to pay in 16K - but because of tax deducted at source I've only got 12K in my bank account. I borrow 4K, pay in 16K and once I get the 4K back from the taxman I repay the borrowing (from a wealthy friend who doesn't want interest )

Scenario 2:

I've got 12K in my bank account. I pay it all into my pension. The pension reclaims 3K - so there's now 15K in there and I get 3K back from the taxman.
Now I pay that 3K in, the pension reclaims 750 - so there's now 18750 in there and I get 750 back from the taxman
Now I pay in that 750, the pension reclaims ~200 - so there's now ~19700 in there and I get ~200 back from the taxman
Now I pay in that 200, the pension reclaims 50 - so there's now ~19950 in there and I get 50 back from the taxman.

Repeat for an infinite number of steps
... so there's now 20K in there

At the end of the day you end up with 20K in the pension either way, just one way gets it all in in one year, the other requires an infinite number of years to converge...

[Jupiter01]

I was thinking of a different scenario and again, possibly misunderstanding.
If a high rate tax payer pays into the pension, they get the auto top up in the pension and then claim further relief via the tax return. In general terms, I think you get 20% automatically and then a further 20% (ish) via the self assessment claim. Let's assume that in this instance the 20% claim via tax return is worth £10k. You can then take this 10k, put back into the pension and endlessly continue with this cycle in subsequent years. Hence the return on your principal amount is way more than 40%. Agree?

[someone]

That's scenario 2 in my example. You actually get 25% of the amount paid in as tax relief (assuming 40% taxpayer) and the pension company also gets 25% tax relief added.

T = (x + x/4) + (x/4 + x/16) + (x/16 + x/64) + ...

T is total in pension after infinite number of years of reinvesting the pension relief. x is the amount you contribute into the pension in year 1.
First term in series is contribution plus tax relief the pension claimed in year 1, second term in series is the tax relief you got in year 1 paid into the pension in year 2 plus the tax relief the pension claims, etc

Expanding the brackets.
T = x + x/4 + x/4 + x/16 + x/16 + x/64 + ...

adding terms with the same denominator. (note that the denominators still increase by a factor of 4 each time)
T = x + x/2 + x/8 + x/32 + ...

Extract a factor of x/2 from all terms except the first one.
T = x + x/2(1 + 1/4 + 1/16 + ...)

Rewriting as a series of powers.
T = x + x/2(1+ 1/4 + (1/4)^2 + (1/4)^3 ...) [1]

Considering only the infinite series in the brackets:
Using the result that 1+x+x^2+x^3+... = 1/(1-x) we get

T = 1+ 1/4 + (1/4)^2 + (1/4)^3 ... = 1/(1-1/4) = 1/(3/4) = 4/3

Substituting 4/3 for the infinite series back into [1] we get

T = x + x/2( 4/3 )

simplifying.
T = x + 2x/3

I.e. the infinite series sums to he same value as the initial payment plus 2/3 of the initial payment.

So going back to my original example where you had 12K available, 2/3 of 12K is 8K so the infinite series sums to 20K - which is what scenario 1 achieved by borrowing 4K temporarily in year 1.

[someone]

T = 1+ 1/4 + (1/4)^2 + (1/4)^3 ... = 1/(1-1/4) = 1/(3/4) = 4/3

This line should not have had a "T =" at the start.

[Jupiter01]

Thanks for explaining that. My key takeaway from the expanded detail on scenario 2 is that if you put in 12k of your own money, you will eventually end up with 20k. That equates to 65% "free money".