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2 Year Plan

Hello,
I have a plan to possibly be Mortgage free at the end of my current deal if everything goes to plan.
I currently have 18 Months left of a 4.58% Nationwide deal with a remaining balance of £21000. I have an overpayment max each year of £7850. I am overpaying each month £500 (£6000 a year).

If I pay a one off payment of £1850+£500 and then continue overpaying each month as well would I be correct in thinking that in around 18 Months I would have around £5000--£6000 left outstanding when my deal comes to an end? I could then pay off the remainder with savings without having another deal?

Does this sound sensible or am I missing something? As I'm trying to explain to wife this is the quickest way for us to be Mortgage Free.

Many Thanks
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