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Check the terms associated with overpaying - you may be able to underpay in future to undo the overpayments, although that might need prior approval which may not be guaranteed.
We're overpaying slightly which should get us to a 60% LTV by the time remortgaging becomes plausible. The early exit fees for our fix are so high that at the moment it wouldn't make sense.
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We're overpaying by around £200/month, the overpayment goes against the capital rather than the interest, and therefore reduces the interest by a fair amount - and the total amount we're paying is the same as it was before we remortgaged for a lower interest rate, we just kept the payment the same rather than dropping it by the amount we saved.
Seemed sensible, I'd love to get shot of the mortgage as early as possible.
It's only debt. Just more of it.