The more money you put down, the smaller the mortgage. Using a 30 year fixed rate mortgage at 5.25%, the factor is 5.52 or $552 for every $100,000 of mortgage. How much you save every month depends on how much more you put down. Its basically a math problem.
The answer to your question then is $8 is not truthful; $5.52 is correct.
The real question is how much should I put down on a home to make the purchase a sound investment and maintain my cash flow so that I am not house poor. With interest rates so extremely low, it's very tempting to put little down. BUT....is this financially sound? What happens if you're laid off for a while, cut back on overtime or if you get sick? Dave Ramsey tells us to wait till we have a 10% down payment. I agree. It is never smart to be at a precarious level.
There's another issue - with less than 20% down, you must pay Private Mortgage Insurance (PMI) which is expensive and, as an insurance policy, not a write off. PMI is is often figured at 1.25% of the mortgage which is a good amount to have to spend. Plus qualifying for a mortgage with PMI is a lot tougher,
With investing, it's always good to be diversitied. If all of your money is in one house, that's not diversified. It is very tempting to mortgage as much as you can with such historically low rates but it's never smart to have all your eggs in one basket. It's not just a question of what you can earn in other investments; it's also a question of being diversified.
You have to examine what you can really do. It may be smarter to take less of a mortgage or more. It's very subjective and depends on your personal situaiton. However, taking on too much debt, having to pay large PMI fees and not being diversified is, in my view, a recipe for disaster.
If you have an accountant, ask your accountant for advice. Go to your banker and ask them. It's always a good idea to get the thoughts of professionals and you should do your own homework. If you're putting down 20% and can do 23% at a time that you can take that 3% and get a 9% yield, then that makes sense as the yield is significantly more than the 5.25% mortgage. But, if you are moving below 20% to get a higher rate of return, it may not be wise at all or even justified when you think about the cost of PMI.
Again, you have to weigh all your options and figure it out like a math problem. My overall advice always is to only make moves that are economically sound. Be careful and you'll be smiling.