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The only reason to overpay is if you fear you might lack willpower
I overpaid because it saved me money on the mortgage without needing to make money by using the money some other way. It's almost a sure thing rather than hoping your investments increase in value, which looking at recent history you'd be in trouble with.
This is probably truer now that interest rates are higher. Sure you can make more money with investments but your mortgage will cost you more.
This may be a stupid question but as someone who is in the following situation:
I'm not sure how to go about the next period until the end of the fixed mortgage. Should I continue to pay the minimum and invest the rest on the basis that the expected return should be greater over the next 5 years or should I look into overpayments?