I thought it'd be useful to repost a previous comment.

For a clearer understanding, it helps to decouple the monetary system and the banking system and look at the options for each. Below are the possible combinations in the form:
Monetary system; Banking system; stability; historicity

1. Gold standard; 100% reserve banking (or usually no banking); stable; historical (first)

2. Gold standard; fractional reserve banking; unstable (no bullion lender of last resort); historical (1694 in England - around 1930 everywhere)

3. Fiat money; fractional reserve banking; stable (as long as central bank is willing to print currency as needed); historical (since around 1930 everywhere)

4. Fiat money; 100% reserve banking; stable; theoretical (Simons 1934 and Fisher 1935).

Heretofore, I refer to system 1 as pure precious metals-based (actually, silver has a longer and richer monetary history than gold), and to systems 2, 3 and 4 as "soft" (should be "funny money" in gold bugs's jargon).

Of note, the biblical prohibition of interest:

Ex 22:24 - "If you lend money to one of your poor neighbors among my people, you shall not act like an extortioner toward him by demanding interest from him"

Lev 25:37 - "You are to lend him neither money at interest nor food at a profit."

Ez 18:8 -"if he does not lend at interest nor exact usury..."

was issued when the monetary system in effect was pure precious metals-based. And it applies only to that system, so that it is legitimate to earn interest from soft monetary systems. That's because the properties of the currency (the entity performing the functions of money) are fundamentally different between pure pm-based systems (where gold and silver have to be mined), and soft systems (where central banks can easily print bills and even more easily create their electronic equivalent).

Below I try to show that:

1. The existence of a widely available, RISK-FREE interest bearing investment requires a "soft" monetary system.

2. For that investment to also yield a REAL positive interest rate, real economic output must grow at that rate or higher.

To demonstrate the first point, let 's assume we have a pure gold system. How can some person or institution make a risk-free promise to anyone to pay them interest on the gold they initially lent (plus the principal at maturity)? By one of two ways:

a. The borrower has the power to exact ever increasing quantities of gold from subject/victim populations, i.e. to forever expand its share of the total bullion stock. Clearly that cannot last long.

b. If we assume the borrower's share of total bullion stocks to remain constant at most, which is plausible, then we need the total stock of monetary gold to grow exponentially at that rate or higher (which implies that the amount of gold mined each year must grow exponentially at the same rate too). Actually, the cumulative gold production did grow exponentially, only the rate was very low, as you can calculate from the data at page
http://www.gold-eagle.com/editorials_00/mbutler031900.html

Thus, the annual rate of growth of above-ground gold stocks was
0.11 % from 1200 BC to 600 BC and again from 300 BC to 500 AD (see the reason for the biblical prohibition of interest?),
0.05 % during the Middle Ages,
0.59 % during the XIX century, and
1.7 % on average during the XX century (actually it was 1.8 % 1900-1950, 1.6 % 1950-1975 and 1.5 % 1975-2000).

Adding silver to the picture changed the above percentages very little.

(As an aside, this shows that a pure pm-based monetary system would have been deflationary since the industrial revolution, most notably after WWII: during the period 1950-1975 world real GDP increased at a cumulative rate of 4.7%, while world total gold inventories rose at a cumulative rate of 1.6%, so that a pure gold-based monetary system would have caused an annual DEFLATION rate of 3%. In practice, that level of deflationary pressure would have directly prevented the occurrence of that economic growth rate. Which could have been actually good, but that's another story.)

As said, the above figures provide the ceiling for the interest that could be offered by a risk-free investment if a pure gold standard had been in place. BTW, 1.5 % leads to k = 1/67. Clearly, the correlation of higher rates of growth of above-ground gold stocks with higher energy use in the XIX and XX centuries is no coincidence, as modern mining is very energy intensive, which also means that, after Hubbert's Peak for oil, the annual growth rate is bound to get lower and lower.

In a fiat money system, on the other hand, the monetary stock can (and certainly does!) grow exponentially at any rate that suits the keepers of the printing press or its electronic equivalent, so the government can promise beyond any risk to anybody to return them any nominal interest rate below that.

Now comes the second point: how do you insure that the nominal interest earned (plus the returned principal) allows the lender to buy more REAL goods and services than the principal initially allowed them to, in a fashion of a certain annual real rate? By having the amount of available goods and services grow exponentially at a rate that fulfills:

(1 + yGR) = (1 + RIR) (1+MGR) / (1 + NIR)

where
yGR: real Net National Income Growth Rate (approx real GDP Growth Rate)
RIR: Real Interest Rate
MGR: Monetary stock Growth Rate
NIR: Nominal risk-free Interest Rate

Since MGR >= NIR as said above (to make the investment yielding NIR risk-free),
it follows that the real GDP growth rate must be >= the real interest rate.

(BTW, the last condition holds for any monetary system, hard or soft, and it comes from the Fisher Equation of the Quantity Theory of Money, M V = P y, assuming constant V. See below.)

The "good" news, then, is that after Hubbert's Peak, since real GDP Growth rates will become negative for a long time, so will real "risk-free" interest rates, and therefore there will be no financial incentive for clearcutting the forest.

Calculation of the real interest rate:

Again from the Fisher Equation of the Quantity Theory of Money:
M V = P y,
where we assume constant V.

P = M V / y

At t=0, let be:
y0 the real Net National Income (can be substituted by real GDP, since we will deal with its growth rate, which will not differ substantially)
M0 the monetary stock (M1 or M2 depending on country)
P0 the price level = M0 V / y0

Let's call Real Purchasing Power at t=0 what an initial amount A0 can buy:
RPP0 = A0 / P0 = A0 y0 / M0 V

Let that initial monetary amount A0 be invested in a risk-free vehicle that yields a nominal interest rate NIR.

At t=n, we have:
yn = y0 (1+yGR)exp(n)
Mn = M0 (1+MGR)exp(n)
Pn = Mn V / yn
An = A0 (1+NIR)exp(n)

where
yGR: real Net National Income Growth Rate (approx real GDP Growth Rate)
MGR: Monetary stock Growth Rate

How much can An buy at t=n?
RPPn = An / Pn = A0 (1+NIR)exp(n) y0 (1+yGR)exp(n) / [M0 (1+MGR)exp(n) V]
RPPn = RPP0 (1+NIR)exp(n) (1+yGR)exp(n) / (1+MGR)exp(n)

Now, you want RPP to grow at a certain annual Real Interest Rate, RIR, so:
RPPn = RPP0 (1+RIR)exp(n)

From the last two equations:
(1+RIR)exp(n) = (1+NIR)exp(n) (1+yGR)exp(n) / (1+MGR)exp(n)

Taking the nth root:

(1+RIR) = (1+yGR) (1+NIR) / (1+MGR)

As said above, for an investment vehicle that yields a nominal interest rate NIR to be risk-free, NIR has to be <= MGR (otherwise it needs to capture an ever greater share of the monetary stock).

That implies RIR <= yGR