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> I’ve heard of this before, but I’m still puzzled by the logic of a loan that never gets paid off. Was this just a bad idea, or does this still happen It soun

> I’ve heard of this before, but I’m still puzzled by the logic of a loan that never gets paid off. Was this just a bad idea, or does this still happen It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation. i.e., suppose inflation is 100%, this means prices will double every year, and the real value of a nominal amount will halven every year. So $100 today, will be worth $50 (in today's money) in a year from now. A year later (2 years), a $100 then will be worth $25 in today's money. Another year later (3 years) it'd be worth $12.5. And so on. As you can see, a nominal future payment, say $100 in 300 years, will start to approach zero. Of course interest rates aren't quite that high, but it's just to get the point across. The interest rate is essentially a discount rate, which lets you value a future amount of money, in today's prices. In the above example, $100 in 3 years would be worth 100 / 2^3 = 12.5 This means that an infinite series of payments (perpetuity) can be calculated as well by simply taking the payment divided by the interest rate to discount it with. So at an interest rate of say 5%, a $100 per year infinitely, would be worth $2000 today. In other words, in a world with 5% interest rates, you'd be indifferent to receive $2000 today, or $100 ad infinitum. They have the same present value.

bawolff 6y ago
Well we have a constant rate of inflation in modern times, how true was that 300 years ago?
- boltzmann_ 6y ago
  > constant Yeah about that..
tantalor 6y ago
Do you know what website you're on? You should have used $128 or $256.
- WJW 6y ago
  Real hackers are not limited to numbers that are powers of two.
  - TimTheTinker 6y ago
    Real hackers maintain their ability to hack decimal architectures.[0] [0] https://en.wikipedia.org/wiki/IBM_7070 https://en.wikipedia.org/wiki/IBM_7070
tzs 6y ago
> It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation. Is it really due to inflation? Even without inflation, wouldn't there still be interest on loans to compensate the lender for not having the use of their money and for the risk that the loan will not be paid back. The present value of a future payment would thus still be discounted, and a stream of payments under a fixed interest rate would still lead to a convergent geometric series for the present value of the total stream.
- lordnacho 6y ago
  Yes it's due to the interest rate, which is loosely connected to inflation. But you're right, even with no inflation, you'd discount by future interest rates, leading to a finite number.
- IkmoIkmo 6y ago
  You're right. I should've just stuck to 'discount rate' instead of interest or inflation. But that's a little too abstract for some. In finance interest rates are typically used for the discount rate. But discount rates can be something else that's not directly related to interest rates, too. For example, suppose I buy gold and it appreciates in value by 10% per year. You could in a way call that inflation (inflation of the price of gold, typically due to inflation of the money supply). And if you were to calculate the value of x amount of gold in one year, in this case you'd use the inflation rate of 10% to discount it to the present value. I should've said discount rates, and in general discussions it's fine to speak of interest rates. Should not have mentioned inflation as it's confusing and often different from the discount rate.
tantalor 6y ago
> simply taking the payment divided by the interest rate to discount it with Looks right, but do you have a proof?
- smabie 6y ago
  We have an infinite series such as: S = sum from (i=1) to infinity of [a^i] we can then multiply by a on each side: aS = sum from (i=1) to infinity of [a^(i+1)] Simplify/cancel out to: aS = S - a a = S(1 - a) S = a / (1 - a) where a = 1 / (1 + R) so $100 perpetuity with R = 5%: a = 1 / (1 + 0.05) = 1 / (1.05) $100 x (1/1.05) / (1 - (1/1.05)) = $100 x 1 / (1.05 - 1) = $100 / 0.05 = $100 / 5% = $2000
  - chadcmulligan 6y ago
    I've always thought this was the most useful equation I learnt at school - S = P (1+i)^n P - Principal S - Sum i - interest rate p.a. n - the number of years
    - smabie 6y ago
      I always liked 58008
thaumasiotes 6y ago
> In essence an infinite set of future payments has a finite present value, due to inflation. Inflation counts, but this would still be true in the presence of strong deflation. A set of future payments has a finite present value due to the fact that the same amount of purchasing power is worth less in the future than it is right now, "time discounting".
- URSpider94 6y ago
  Yes and no. In the case of true deflation, interest rates can become negative, such that money in the future has more value than money today. In that case, the value of this loan would diverge towards infinity.
  - thaumasiotes 6y ago
    You're making an unfounded assumption about the rate of time discounting.
    - URSpider94 6y ago
      Help me explain where my unfounded assumption is. If the interest rate is negative, that explicitly means that money in the future is worth more than money today. That's the definition of a negative interest rate.
- iggldiggl 6y ago
  Wait, that doesn't make sense now, does it? Deflation means precisely that money will be worth more in the future than it is now, so a future payment stream will correspondingly also be more valuable than cashing out right now. (Which is also why economists often regard it as a bad thing, because it entices people to hold off on spending/investing, thereby slowing down the economy). Now I agree that as such money now is somewhat more valuable than money later in nominal terms simply due to the uncertainty of the future, and it's probably unwise to bet on everlasting strong deflation, but at least in the short or medium term I'd say strong deflation could certainly overcome even these built-in inflationary tendencies.
deleted 6y ago
[deleted]

bawolff 6y ago

Well we have a constant rate of inflation in modern times, how true was that 300 years ago?

boltzmann_ 6y ago
> constant Yeah about that..

tantalor 6y ago

Do you know what website you're on? You should have used $128 or $256.

WJW 6y ago
Real hackers are not limited to numbers that are powers of two.
- TimTheTinker 6y ago
  Real hackers maintain their ability to hack decimal architectures.[0] [0] https://en.wikipedia.org/wiki/IBM_7070 https://en.wikipedia.org/wiki/IBM_7070

tzs 6y ago

> It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation. Is it really due to inflation? Even without inflation, wouldn't there still be interest on loans to compensate the lender for not having the use of their money and for the risk that the loan will not be paid back. The present value of a future payment would thus still be discounted, and a stream of payments under a fixed interest rate would still lead to a convergent geometric series for the present value of the total stream.

lordnacho 6y ago
Yes it's due to the interest rate, which is loosely connected to inflation. But you're right, even with no inflation, you'd discount by future interest rates, leading to a finite number.
IkmoIkmo 6y ago
You're right. I should've just stuck to 'discount rate' instead of interest or inflation. But that's a little too abstract for some. In finance interest rates are typically used for the discount rate. But discount rates can be something else that's not directly related to interest rates, too. For example, suppose I buy gold and it appreciates in value by 10% per year. You could in a way call that inflation (inflation of the price of gold, typically due to inflation of the money supply). And if you were to calculate the value of x amount of gold in one year, in this case you'd use the inflation rate of 10% to discount it to the present value. I should've said discount rates, and in general discussions it's fine to speak of interest rates. Should not have mentioned inflation as it's confusing and often different from the discount rate.

tantalor 6y ago

> simply taking the payment divided by the interest rate to discount it with Looks right, but do you have a proof?

smabie 6y ago
We have an infinite series such as: S = sum from (i=1) to infinity of [a^i] we can then multiply by a on each side: aS = sum from (i=1) to infinity of [a^(i+1)] Simplify/cancel out to: aS = S - a a = S(1 - a) S = a / (1 - a) where a = 1 / (1 + R) so $100 perpetuity with R = 5%: a = 1 / (1 + 0.05) = 1 / (1.05) $100 x (1/1.05) / (1 - (1/1.05)) = $100 x 1 / (1.05 - 1) = $100 / 0.05 = $100 / 5% = $2000
- chadcmulligan 6y ago
  I've always thought this was the most useful equation I learnt at school - S = P (1+i)^n P - Principal S - Sum i - interest rate p.a. n - the number of years
  - smabie 6y ago
    I always liked 58008

thaumasiotes 6y ago

> In essence an infinite set of future payments has a finite present value, due to inflation. Inflation counts, but this would still be true in the presence of strong deflation. A set of future payments has a finite present value due to the fact that the same amount of purchasing power is worth less in the future than it is right now, "time discounting".

URSpider94 6y ago
Yes and no. In the case of true deflation, interest rates can become negative, such that money in the future has more value than money today. In that case, the value of this loan would diverge towards infinity.
- thaumasiotes 6y ago
  You're making an unfounded assumption about the rate of time discounting.
  - URSpider94 6y ago
    Help me explain where my unfounded assumption is. If the interest rate is negative, that explicitly means that money in the future is worth more than money today. That's the definition of a negative interest rate.
iggldiggl 6y ago
Wait, that doesn't make sense now, does it? Deflation means precisely that money will be worth more in the future than it is now, so a future payment stream will correspondingly also be more valuable than cashing out right now. (Which is also why economists often regard it as a bad thing, because it entices people to hold off on spending/investing, thereby slowing down the economy). Now I agree that as such money now is somewhat more valuable than money later in nominal terms simply due to the uncertainty of the future, and it's probably unwise to bet on everlasting strong deflation, but at least in the short or medium term I'd say strong deflation could certainly overcome even these built-in inflationary tendencies.

deleted 6y ago

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