If everyone’s money savings suddenly doubled overnight, there would be no effect on real interest rates, and likely little effect on relative prices, which is all that is important. However, rising prices might drive up nominal interest rates.
The original poster committed a fallacy. The increased demand arising from new money should not simply signal to businesses to produce more stuff. Profit margins do this. If everything has increased demand, all prices, including producer prices, will increase. Profit margins should stay about the same, and few will be persuaded into changing their business.
One thing it would do is reduce the difficulty of pre-existing debtors to repay, while diminishing the real gains their creditors make on their loans. Interest rates will change to reflect this in real terms; however, if inflation is continuously surprisingly pursued to creditor’s dismay, this will have the effect of reducing time preference, reducing savings.
New money in real life has two important characteristics. One, it is not equally distributed relative to money savings. This means that new money creates specific winners and losers. It’s best to be closest to the source of the money. This alters the structure of production.
Two, most new money originates in the banking system, which drives down interest rates. Thus, while time preference is actually reduced, interest rates also go down, a fundamental mismatch in the market’s signals to determine production. This is the root of the business cycle. Interest rates and savings rates do not coincide, creating an unsustainable foundation for new investments.
Once the new money is loaned out, it can no longer effect interest rates, and they will rise to reflect time preference again, even if the new money is never removed from circulation. If new money is continuously produced and put into circulation through the credit market, it will continuously keep interest rates lower than they should be.