Early redemption of a repayment mortgage - who is mad, me or HSBC?

Ade_In_Hove

Hello,
First of all I realise these are difficult times and some people are struggling financially, so I hope anyone reading this who is in that situation is seeking any advice that is available and that you resolve any issues without too much anxiety.
The central theme of my question is that intellectually I had always thought (subject to any early repayment fees) if you pay off a repayment mortgage early you save money because you don't have to pay the interest on borrowing the money for the rest of the term.  In days gone by - in the 1990s - I know you generally paid the interest off first, before any capital, but I understood those days are behind us.
I have repayment mortgage with HSBC with a term that ends on 3rd June 2036 (in about sixteen years).  I'm not sure what the exact interest rate is (I can't find it on their website and recent documentation has disappeared - but I realise it's low!) - the monthly repayments are £1,237.44.  Every month, depending on the number of days in that month, I am paying around £280 in interest for borrowing the remaining capital.  So I think - if I repay that capital today I should avoid 16 years of around £280 monthly interest payments - or 16 x 12 x £280 = around £53,000.  There is no early redemption fee payable.
At the end of August the balance was £207,011 and I pressed the button on HSBC's online banking website for an early redemption quote effective 1st October 2020.  The document I received indicated the amount I would need to pay off on 1st October 2020 would be £207,717.  That didn't seem right, so I eventually managed to get through to one of HSBC's mortgage advisors on the phone.  Unfortunately, I was unable to get my point across to this agent (perhaps because I am mistaken) - they provided me with an early redemption figure again pretty much the same as the total balance.
On November 11th I used the MSE overpayment calculator and it tells me that if I make a lump sum repayment of £165,000 in January 2021 I will save £31,139 in interest payments.  I realise this is computer generated and relies on certain assumptions, but it does suggest a disagreement with HSBC and an agreement with me.
What are people's thoughts on this please?
By the way, I am OK in terms of mortgage and general financial advice thanks - I don't want to attract offers of help, just opinions on whether early redemption of a repayment mortgage does or does not save money.  Oh, and I do highly rate HSBC as a bank and lender - I just disagree with them on this point.  Thank you!!

[Deleted User]

You're misunderstanding how interest works. 

It's not a flat sum each month for the duration of the mortgage.  Interest is calculated daily on the outstanding balance, so as the balance drops, so does the interest.

If your redeem early, the settlement will be your current balance or thereabouts - just as they have told you.  They don't give you any of the interest you've paid back as that was the interest required for borrowing the money.

Thrugelmir

As interest is calculated daily and charged monthly. Unless you view the balance outstanding on the day interest is charged to the account. You'll always be looking at a lower figure than is required to redeem. 

Throwaway1

Your interest payments won't be 12 x the amount you are paying now for X amount of years as the interest rate will fall every time you chip some off the captial (and also whenever your interest rate changes if a fixed term agreement ends or the variable rate changes). If you have no early repayment charge then the amount you see as outstanding now (plus a few days/weeks of interest that has accrued but not yet been added on) is the amount you need to pay to be mortgage free. If it actually takes you another 16 years to pay it off, the total amount you will pay is the amount you see as outstanding now plus all the interest that gets added on over that 16 years. So, paying it off now saves you money as you won't be paying all the interest that will be added over that time that is on top of the figure you see now (as the figure you see now does not include the interest).