# Can interest be payed without first taking on more, new debt?

In general, the person that lends out Money will ask interest payment. In the modern economy, bank credit *creates* money in the form of debt, while repaying debt *destroys* money.1 While the debt money is created, the interest that needs to be payed for the service is not. Some propose that it is *impossible* to pay that interest without someone (else) taking on more debt first. However, by considering money as a flow in a micro-scale closed system, it is easily shown that debt plus interest can be payed back without any problem in most cases. It is explored here what is necessary to “close” the debt and how time and interaction between this type of systems affects the flow and the behavior of money.

## The money system

The story is about the creation of money by lending the principal to an actor by another actor (the bank), the destruction of money by repaying the principal and paying between actors that include interest payments. To explain this behaviour, a simple money debt based money system without a central bank is perfect.

# Scenario without necessity for additional debt

This is a free adaptation of the story on Positive Money2 that debunks the fact that it is mathematically impossible to pay back interest.

Alice the entrepreneur wants to borrow 100 credits. George agrees and demands 10% interest. The 100 credits are called the *principal * of the loan, due in a year. The 100 credits are added to Alice's balance and in one year from now, Alice needs to repay George 100 credits and an extra 10 credits as interest: a total of 110 credits.

Alice first buys a machine from Pete (50 credits) that enables her to create stuff. She also buys bread from Bob (10 credits). During the year, Bob, Alice and Pete exchange money on their balances for goods. Alice makes "stuff", Bob bread and Pete machines. Naturally, Alice makes sure she has the 100 credits back in time to repay her debt.

Just before the principal and interest are due, Alice pays George the interest in advance: her balance becomes 90 and George's 10 credits. Now George buys 10 credits of breads from Bob and Bob uses that to buy 10 credits of "stuff" from Alice, so Alice, again, has 100 credits. Then she repays George, who dutifully resets her balance to zero.3 In numbers:

Action | Day | Balances | |||
---|---|---|---|---|---|

George | Alice | Bob | Pete | ||

Alice gets loan with principal of 100, George increases her balance with principal |
1 | - | 100 | - | - |

Alice buys machine from Pete | 2 | - | 50 | - | 50 |

Alice buys bread from Bob | 2 | - | 40 | 10 | 50 |

Arbitrary situation during year | 42 | - | 15 | 35 | 50 |

Alice ensured she has money back | 361 | - | 100 | - | - |

Alice pays interest to George | 362 | 10 | 90 | - | - |

George buys bread from Bob | 363 | - | 90 | 10 | - |

Bob buys stuff from Alice | 364 | - | 100 | - | - |

Alice pays principal of 100, George decreases her balance with prinicpal |
365 | - | - | - | - |

## What's wrong with this story?

Even though the story proves that it is not mathematically *impossible* to repay debt and the additional interest: it is a rather contrived story: all inhabitants must make the right decisions at the right time. Reality is messy, so this "model" of a society is too simplistic. Let's make it more interesting!

# Scenario, where interest is added to bank's capital

**Work in Progress as of 2017-09-09**