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Overpayment Advice & Safety Net

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Hi everyone, I'm after some advice with regards to if I should make a lump sum over payment...

I bought my first house at the end of May last year for £160k, I put a £40k deposit in taking a £120k mortgage over 25 years (£600 p/m). Im on a 2 year fix with Natwest and off the top of my head its 4.1%.

My aim is to try and get me LTV to 60/40% for when I am looking for deals in 18months so I can get a good rate. This means paying off £24k, my mortgage allows 10% overpayment per year so I can do just under £12k this year.

I have about £56k in savings with the best account earning around 2.81% interest until October.

What kind of savings should I be looking to hold on to? I may need a new car in the future, say £5k and maybe £2k on some home improvement.

Is it advisable for me to make this overpayment, seems to make sense on the guides I have read...

Thanks

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