[neilk]

I think the term for this is "full-reserve banking" or "100% reserve banking".

The Wikipedia page only talks about governments that have occasionally flirted with the idea, and economists who have debated its merits as a regulatory policy. I haven't found any bank that claims to be doing it.

https://en.wikipedia.org/wiki/Full-reserve_banking

You might be thinking about this the wrong way. It's not that banks are tempted to invest, it's that this is the whole business model, and it's even part of how most governments stimulate (or throttle) economic activity. Ultimately banks get a charter to multiply money, at a rate that the government thinks is good for everyone.