Decide Whether to Overpay Your Mortgage or Invest the Surplus

Overpay or invest is one of the few personal finance decisions where the maths is fairly clear but most people still end up doing neither because the decision is harder to make than it looks. This sets out the framework for your specific numbers and tells you which direction makes more sense.

I have some surplus money each month and I am trying to decide whether to overpay my mortgage or invest it. I want a clear framework for making this decision for my specific situation.

My situation: mortgage rate: [state your rate], remaining mortgage term: [state it], approximate monthly surplus: [state it], whether I have an emergency fund: [yes/no and size], other debts: [list any]

Help me think through this: what the two options actually do mathematically over the relevant time horizon, what other factors beyond the maths should influence the decision (risk tolerance, security, flexibility), and a clear recommendation for my situation. Note: this is for general educational purposes, not regulated financial advice.