# Cash and reserves

## The origin of interest​

Taking the US Dollar as a representative example, its short term interest has averaged 5% over the last 50 years, which compounds to growth by a factor of more than 100x over a 100 year period. Clearly, over such a time period, the interest paid out quickly becomes greater than all money at the start of the period - therefore it must be that interest is paid from newly created money. Indeed, major central banks1 pay short term interest with money which they create2.

There is however a large gap between the interest being paid on currencies of advanced economies (essentially 0% today) and the rate at which their money supply grows (which remains at or above historical levels). The Liquid Interest Bearing Reserve Accounting system closes this gap, with all money supply growth necessarily paid as interest, on either Cash, Bonds, or Stake.

Moreover, the rate at which this money supply grows to generate interest is permanently fixed at 6% annually. This 6% rate is still below the average money supply growth rate consistent across advanced economies3. Interestingly, some central bank which are setup as corporations, such as the Federal Reserve and Swiss National Bank, do pay 6% out even today4, but only as dividends to their shareholders.

## Stability from reserves​

A defining feature of currency is price stability. The surest way to achieve stability is with a peg: holding a unit of a reserve currency for each unit of local currency. Pegging to a unit which another central bank controls is a losing proposition however, as they can print more money at no cost, thereby misappropriating some of your purchasing power, while you have no offsetting recourse.

Taking this into account, the Liquid Interest Bearing Reserve Accounting system allows the price of its Cash asset to fluctuate, but only as a prescribed function of supply and demand. When Cash units are sold into circulation, the system accumulates reserves in stablecoin US Dollars (specifically Dai), which are used exclusively to defend the price of Cash and continuously auditable.

## Cash mechanics​

The reserve price of Cash $p$ is specified as a function of, $M$, the amount of Cash in circulation5, and $R$, the amount of Dai reserves, namely

$p = \max \left\{ \frac{3 R}{M + \frac{10^{10}}{9} - {\left( \frac{27}{10^{15}} M + \frac{3}{10^5} \right)}^{-2} }, \frac{R}{M} + \frac{1}{10 \ln(10)} \left( 1 - \frac{\ln(M + 1)}{M} \right) \right\}$

which is accordingly in units of Dai. At all times the reserves are made available to buy back Cash at price $p$, and reserves are not used for any other purpose. While there is Cash out of circulation, it is available for sale at price $p$, so that $p$ fully determines the market price of Cash.

At launch, there are 10 billion units of Cash, with price $p = 1$. From there, the price is fully determined by the demand for Cash and Bonds. The tool below simulates the Cash market under the scenario where demand equals the historical demand for a chosen stablecoin6.

The total return realized on Cash is the combination of price move and interest accrued. The total return series plotted below is for a scenario where no Bonds are issued. The actual return on Cash can be lower in general, while the return on Bonds can be higher, and both will always be above the return from Cash price move alone.

1. Including the US Federal Reserve, European Central Bank, Bank of Japan and Bank of England.
2. This is interest on the reserves commercial banks have deposited with the central bank (discussed eg. here).
3. As shown in the chart on the front page.
4. Refer to Fed and SNB documents.
5. In the presence of Bonds, $M$ then counts the net amount of Cash sold into circulation, plus the interest accrued on Cash and Bonds.
6. As all these stablecoins track one US Dollar, equal demand means that the amount of reserves for the simulated Cash is set to the stablecoin market capitalisation.