It all started with a random tweet that compares Chuck E. Cheese tokens and Bitcoin. The mouse-in-chief (or whoever controls its account) decided to join the fray with a bitter tweet that eventually went semi-viral.
[...] Multiple arguments went into play — from the BTC price that recently breached $10,000 once again to coin's 24/7 availability (Chuck E. Cheese cannot relate).
[...] It's not exactly clear what Chuck E. Cheese was trying to achieve with this tweet, but it definitely got what it desperately needed — media attention.
Multiple outlets, including the Wall Street Journal, have already covered what can be considered one of the strangest Bitcoin debates you will ever see on Twitter.
https://u.today/chuck-e-cheese-mouse-gets-roasted-by-cryptocurrency-enthusiasts
The tweet that started it all:
Ryan Hoover
@rrhoover
Chuck E Cheese tokens are cool and all but I'd rather earn Bitcoin
(Score: 0) by Anonymous Coward on Saturday July 06 2019, @04:40PM (7 children)
It's exactly like a normal mortgage id imagine.
(Score: 2) by Rupert Pupnick on Saturday July 06 2019, @05:16PM (6 children)
Well, take a look at the equation that gives monthly payment M as a function of principal P, monthly interest rate r (expressed as a decimal fraction), and number of payments n:
M = P[r(1+r)^n/((1+r)^n)-1)]
When r=0 (an interest free loan), instead of getting M=P/n, you get 0/0. So I don't trust this for negative values of interest rate. What does a banker do in this case?
(Score: 0) by Anonymous Coward on Saturday July 06 2019, @06:04PM (3 children)
Gotta look into how that equation is derived. It must assume r> 0 somewhere to simplify things.
(Score: 2) by Rupert Pupnick on Saturday July 06 2019, @09:01PM (2 children)
OK, I eagerly await the results of your research! ;)
(Score: 2, Informative) by Anonymous Coward on Saturday July 06 2019, @10:28PM (1 child)
I didn't work out the consequences but probably here:
http://www.hughcalc.org/formula_deriv.php [hughcalc.org]
(Score: 2) by AthanasiusKircher on Sunday July 07 2019, @12:26PM
No, that's not the problem. Read through your link. The problem is the assumption that you're dealing with a geometric series, whose sum is given by the standard formula for geometric series.
But that sum doesn't work when the common ratio of the series is 1, i.e., when interest doesn't compound and the amount of interest paid each month is the same (zero in the case of interest =0%).
Essentially the formula for loan payments looks a bit like what happens when you run compound interest "in reverse," since the part of the loan principal you don't pay until the end effectively gets compounded interest all the way back to the beginning of the loan. If there's no interest charged, it doesn't compound, so the amount of your monthly payment is simply the principal divided by the number of payments.
The assumption you quote (where Q=0 at the end because the loan is paid off) is still true, obviously. But the problem is the sum of the series doesn't equal equation 2 in the case where the interest rate is zero... The sum of the series will just be number of payments times M.
(Score: 1) by sensei_moreh on Sunday July 07 2019, @12:54AM (1 child)
It works for any non-zero rate of interest, positive or negative
Geology - It's not rocket science; it's rock science
(Score: 2) by Rupert Pupnick on Sunday July 07 2019, @12:58PM
Thank you sensei and AC. The geometric series on which the mortgage formula is based doesn’t work for r=0, but does work for all other values positive and negative. I picked an interest rate of 6% because that makes r=.005, and did some arithmetic, and here’s what I got:
For a 30 year mortgage on $100,000 of principal at +6% the monthly payment is $628.
For a 30 year mortgage on $100,000 of principal at 0% the monthly payment is $312.50.
For a 30 year mortgage on $100,000 of principal at -6% the monthly payment is $125.
Note for this last case the bank only receives a total repayment of only 40k on the original 100k loan.
I understand that negative interest rates tend to only emerge in a deflationary economy, but isn’t this still giving money away? Is it because 40k is worth more in 30 years in some sense than 100k now? 30 years is a long time to be making that sort of a bet. I know the negative interest rates quoted in the article were much lower in magnitude, but would a bank really do this?