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+Demurrage in Ripple Currencies
+==============================
+
+[Demurrage](http://en.wikipedia.org/wiki/Demurrage_%28currency%29) is a
+negative interest rate on assets held that represents the cost of
+holding those assets. Ripple supports currencies that have interest or 
+demurrage rates built into the currency definition, such as 
+"XAU (-0.5%pa)". Each currency-rate combination is treated as a completely
+distinct currency for purposes of pathfinding and order books.
+
+A gateway that wants to charge demurrage for holding assets (such as 
+gold) can issue a custom currency representing that asset with the 
+demurrage rate built-in. This is reflected in a different hex 
+representation for the demurraging currency. Client applications should 
+represent a demurraging currency by displaying the negative annual 
+percentage rate along with the currency code. 
+
+XRP cannot have demurrage or interest.
+
+Dealing with Demurraging Currencies
+-----------------------------------
+
+The rippled server, and consequently the official global ledger, do not
+track changes in value due to demurrage in the balance of funds. This
+allows demurrage costs to be applied continuously, instead of operating
+on fixed intervals. It also prevents demurrage from inflicting
+significant additional computational and storage load for servers that
+are part of the network. Instead, the fact that particular holdings are
+subject to demurrage is tracked in the ledger by virtue of the custom
+currency codes. Demurrage is calculated on the entire currency as if it
+were interest, according to the following formula:
+
+D = A \* ( e \^ (t/ τ) )
+
+where:
+
+-   D is the amount after demurrage
+-   A is the pre-demurrage amount as recorded in the global ledger
+-   e is Euler's number
+-   t is the number of seconds since the [Ripple
+    Epoch](rippled-apis.html#specifying-time) (0:00 on January 1, 2000
+    UTC)
+-   τ is the [e-folding time](http://en.wikipedia.org/wiki/E-folding) in
+    seconds. This value is calculated from the desired interest rate.
+
+You can think of demurrage in the Ripple Network as similar to
+inflation, where the value of all assets affected by it decreases over
+time, but the ledger always holds amounts in year-2000 values. (This
+representation was chosen as a simplification of the more complicated
+representation where individual holdings could track when the demurrage
+on them started accruing, because this way it becomes easier to
+recognize, exchange, and represent assets with demurrage applied.) Keep
+in mind, this does not reflect actual, real-world inflation: instead,
+it's hypothetical inflation at a constant rate.
+
+### Calculating e-folding time
+
+It is simple to calculate from a targeted demurrage rate in annual
+percent to get a τ value to use in calculating demurrage:
+
+1.  First, subtract the demurrage percentage rate from 100% to get the
+    percentage of initial amount that remains after annual demurrage.
+    Represent it as a decimal. For example, for 0.5% annual interest,
+    you would get 0.995
+2.  Now, take the natural log of that number. For example, ln(0.995).
+    For traditional demurrage (decrease in value over time), this value
+    will be negative.
+3.  Finally, take the number of seconds in one year (31536000) and
+    divide by the result of the natural log operation. The result is
+    your e-folding time in seconds, for example -6291418827.045599
+
+If you're curious: Since an e-folding amount represents how long until
+an investment increases e times, a negative interest rate means that the
+investment would have been worth e times its value that amount of time
+in the past. Alternatively, it means that after that amount of seconds,
+the investment will be worth 1/e of what it used to be.
+
+### Canonical Calculations
+
+For purposes of calculating demurrage consistently across applications,
+the precision used is important. Our canonical source of demurrage
+calculations is ripple-lib. By following these specifications, you
+should be able to reproduce the demurrage results from ripple-lib
+exactly:
+
+First, recall the canonical formula for demurrage:
+
+D = A \* ( e \^ (t/ τ) )
+
+where D is the post-demurrage amount, and A is the pre-demurrage amount.
+For the remainder of the formula, e \^ (t/ τ), we call this the
+"demurrage coefficient". The demurrage coefficient is always relative to
+a specific time, such that demurrage is calculated for the period
+starting at the beginning of the Ripple Epoch (00:00:00 January 1, 2000)
+
+The two directional calculations can therefore be simplified to:
+
+1.  Find the demurrage coefficient for the reference time
+2.  Apply it to the amount to convert
+    1.  To convert ledger values to display values, multiply by the
+        demurrage coefficient
+    2.  To convert display values to ledger values, divide by the
+        demurrage coefficient
+
+3.  Make sure that the converted value can be represented to the desired
+    accuracy. For example, ledger values submitted to Ripple must fit in
+    Ripple's [internal format](https://wiki.ripple.com/Currency_format).
+
+For more information on the necessary precision:
+
+The demurrage coefficient should be calculated entirely in [64-bit
+IEEE754
+doubles](http://en.wikipedia.org/wiki/Double-precision_floating-point_format),
+such as the number types native to Javascript, or the float type
+available in Python. However, there are some additional notes:
+
+-   For purposes of demurrage, one year is defined as exactly 31536000
+    seconds. This is exactly 365 days, with no adjustments for leap days
+    or leap seconds.
+-   The reference time should be specified in seconds, as an integer. If
+    your clock provides a higher resolution, you should truncate the
+    reference time to seconds before using it.
+
+Client Applications
+-------------------
+
+In order to accurately convey amounts in present-day terms, client
+applications must adjust for demurrage. This means a few things:
+
+-   When representing the value of a demurraging currency, the display
+    value should be adjusted to the "post-demurrage" values. (This
+    generally means that display values will be lower than the ledger
+    values.)
+-   When making offers or transactions in a demurraging currency,
+    amounts entered by the user should be adjusted upward, to interpret
+    user input as post-demurrage numbers. (This generally means that
+    amounts written into offers are higher than the user input value)
+
+Client applications must also make sure to distinguish between
+currencies with differing amounts of demurrage, and to display the
+correct demurrage rates for all currencies with such rates. Currently,
+the only Ripple Labs-created client that supports demurrage is Ripple
+Trade.
+
+### ripple-lib support
+
+Clients that are built from
+[ripple-lib](https://github.com/ripple/ripple-lib) can pass a
+`reference_date` as an option to the Amount.from\_human function to
+account for demurrage. This function can automatically convert a
+human-input number to the necessary amount to hold on the ledger to
+represent that value in at a given time. (The amount that is sent to the
+rippled server is the hypothetical amount one would have needed in order
+to have the desired amount after enduring constant demurrage since the
+Ripple Epoch.)
+
+For example, if you're using javascript, you can use ripple-lib utility
+to calculate this manually:
+
+```
+    // create an Amount object for an amount of the demurring currency, in this case 10
+    // pass in a reference_date that represents today, 
+    // which will calculate how much you will need to represent the requested amount for today
+    var demAmount = Amount.from_human('10 0158415500000000C1F76FF6ECB0BAC600000000', {reference_date:459990264});
+
+    // set the issuer -- optional
+    demAmount.set_issuer("rHb9CJAWyB4rj91VRWn96DkukG4bwdtyTh");
+
+    // get the json format that can be used as TakerPays or TakerGets in the order creation
+    console.log(demAmount.to_json());
+
+    // this will output an Amount with ~10.75 as the value for XAU, which is what is needed to create an
+    // effective order today for 10 XAU
+```
+
+
+To calculate how much a given amount has demurred up to today:
+
+```
+    // create a new Amount object
+    var demAmount = Amount.from_json('10/015841551A748AD2C1F76FF6ECB0CCCD00000000/rHb9CJAWyB4rj91VRWn96DkukG4bwdtyTh');
+    
+    // apply interest
+    demAmount = demAmount.applyInterest(new Date());
+
+    // get the current amount:
+    console.log(demAmount.to_json());
+
+Where Does Demurrage Go?
+------------------------
+
+To put it simply, the value that depreciates due to demurrage becomes
+the property of the gateway issuing the currency. This means that, when
+someone holding a balance of currency goes to redeem that currency from
+the Gateway, the amount they get is the post-demurrage amount (the
+"display amount") relative to the current moment in time.
+
+Note that, when the Gateway issues currency with demurrage, it must also
+adjust the values it issues, so that the amount sent to the rippled
+server and written in the ledger is already adjusted for demurrage up to
+the point in time it was issued.
+
+Demurrage and Money-Making Offers
+---------------------------------
+
+Demurrage ensures that particular currencies "drift" in value slowly
+over time, so that the same amount on the ledger is worth increasingly
+less over time when redeemed. (A balance will never go negative, but it
+will get closer and closer to zero value.) However, offers are not
+automatically updated to compensate for demurrage that accumulated in
+the time since the offer was made. This means that, if you are making an
+offer to buy a demurraging currency, you must occasionally adjust your
+offer to ask for higher ledger amounts to get the same post-demurrage
+actual value. However, we expect this to be a complete non-issue because
+the relative value of currencies (especially pseudo-currency commodities
+such as precious metals) fluctuates much faster than typical rates of
+demurrage.
+
+Since Ripple client applications already adjust for demurrage when
+taking human inputs to make an offer, most users will not have to do
+anything different when making offers.
+
+Currency Format Details
+-----------------------
+
+Currency with demurrage or interest is represented as a 160-bit value
+that begins with the value `0x01`. This sets it apart from hashes (which
+are always `0x80` or higher) as well as standard currency (`0x00`) and
+other currency types we may define in the future (`0x02-0x7F`).
+Demurraging currency has the following format:
+
+    01 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
+       CURCODE- DATE------- RATE------------------- RESERVED---
+
+-   CURCODE is the 3-byte currency code, such as "USD"
+-   DATE is no longer used, and should always be 0.
+-   RATE is the e-folding time, formatted as an IEEE Double, represented
+    in hex. For example, -6291418827.045599 becomes "C1F76FF6ECB0BAC6".
+-   RESERVED is reserved for future use. It should always be given as 0,
+    but other values should be accepted for forward-compatibility.
+