Downsize to be mortgage free in 3 years

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Hi, we're in our late 30s and we're thinking about downsizing our 5 bed to a 2 or 3 bed (we don't have any kids). Our current mortgage is £140k and about £60k on the help to buy. We originally purchased the house for £220k 5 years ago and is now worth £300k. Minus what we owe, we are looking at about £100k profit that we can put in as a deposit. We've seen some new builds 2 bed around £150-£170k where our mortgage will be around £60k. We can then take out a 3 year rate and be mortgage free in our early 40s. Would you consider this a good sensible plan to take the profit and downsize? Would a fix rate over 3 years but having a 25 year term would be a better approach knowing the mortgage will be cleared in 3 years (i.e. lower monthly repayments, room to overpay, and room to put money in a savings account. Appreciate you thoughts. I did make a separate post about using downsizing and using £100k to buy/sell through auctions but thought this would be more hassle than its worth. Many thanks. 
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