I've got a mortgage in the UK with a 5 year fixed rate of 1.69% that expires in Dec 2025 and started in May 2021. I've decided to pay it as soon as possible and I'm trying to figure out what's the most efficient way to do that. Every year I'm allowed to overpay 10% of the outstanding balance with the fees for overpaying on top of the 10% being 5% in the first year, 4% in the second, etc. Given that, I'll definitely be able to save more than 10% of the outstanding balance every year, should I overpay all my savings immediately and pay the penalties or should I put my savings over 10% in a savings account and pay them after the 5year product expires?
Just doing the math, if I overpay at the start of the 2nd year, I'd be saving around 4 years of interest 1.69^4=8.15, so in theory I should save 8.15%-4%=4.15% on the extra money I overpay. Following this logic however, it seems less worth overpaying extra after that (3rd year is 1.69^3-3=1.8%, 4th year - 1.69^2-2=1.38% and 5th year - 1.69-1=0.69%) since I might be able to find a savings account/invest in a low risk index fund and get a better return. Is that a correct assumption?
Also, every time I overpay, my monthly payment is reduced, so that the original term doesn't change. With that in mind, should I overpay regularly, e.g monthly, or save and pay in a lump sum at the end of each year? I can't figure out which would reduce the outstanding balance faster.