Paying off mortgage versus Saving the money

I’ve been looking into this as a first time home buyer and commonly people say that the money you put towards your mortgage principal is guaranteed return on your dollar which makes sense, but a lot say you can typically earn more saving for retirement.

What I’m getting stuck on is people keep saying the the return on your extra mortgage principle is equal to your Mortgage rate. So if I have a 4.5% rate then I 4.5% on every dollar extra I pay. But this seems very off to me. The way mortgages work being amortized the interest ends up being far more than 4.5% of the total amount.

For instance a $200,000 mortgage with 4.5% interest for 30 years ends up costing ~$164,000 in interest total. And if you were to pay an additional $100 a month over the required payment you end up saving ~$40,000 in interest and paying off the mortgage in 23 years. That means you spent $27,600 and saved ~40,000 which is much more than a 4.5% return.

I’m guessing I’m just not understanding something or missing something big here. Any insight would be great.

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