OK, I'm not sure this is in the correct sub-forum, but what I have is essentially a math -- interest rate calculation question -- that I just don't seem to be able to think through and I associate investments discussions with math, so ....

Question: If you pay a large, lump sum (say $20,000) towards the principle on a loan (say at 3.3%, since this is what our mortgage is at) will you save exactly the same amount of money as you would earn over the same period of time (say 10 years) as you would if you invested that money in a hypothetical bond that had a 3.3% interest rate?

If there is no difference whatsoever in the $ amount saved or earned (let's not get into taxes and other issues just to keep the calculation simple), would this still be the case if 5 years into the term, we added a second $20,000 towards paying of the principle on a loan or, alternatively, again invested $20,000 in a hypothetical bond again with a 3.3% interest rate?

Intuitively, I'd say there was no difference, because it's a 3.3% interest rate either way. However, is there something I'm not seeing here?