Bitcoin Forum
June 22, 2018, 12:05:16 AM *
News: Latest stable version of Bitcoin Core: 0.16.1  [Torrent]. (New!)
 
   Home   Help Search Donate Login Register  
Pages: « 1 [2]  All
  Print  
Author Topic: Bitcoin loan payment formula (WARNING: MATHS AHEAD!) [FORMULAS FIXED]  (Read 4039 times)
kwhcoin
Jr. Member
*
Offline Offline

Activity: 42
Merit: 0


View Profile
July 16, 2011, 01:08:13 PM
 #21


I get weird numbers. Can you provide an Open Document Spreadsheet with an example?


I did the calculation with some real numbers and included the output of an excel spreadsheet.


Yep, I get the same numbers.
The only thing that still concerns me though is that the lender needs to get (1+i)*(1+d) return on his investment, yet this calculates each k outstanding balance to be paid off as just Bal*(1+i)...

In your example, the loan interest rate is 5% so the lender only needs to get 5% interest on the balance. It may end up "feeling" closer to 8% interest with respect to purchasing power (i.e. 5% interest plus 3% deflation), but the loan interest rate does not include deflation just like a typical 5% loan from a bank in dollars with 3% inflation is still just a loan for 5% even though the inflation makes it feel more like 2% with respect to purchasing power.
1529625916
Hero Member
*
Offline Offline

Posts: 1529625916

View Profile Personal Message (Offline)

Ignore
1529625916
Reply with quote  #2

1529625916
Report to moderator
The World's Betting Exchange

Bet with play money. Win real Bitcoin. 5BTC Prize Fund for World Cup 2018.

Advertised sites are not endorsed by the Bitcoin Forum. They may be unsafe, untrustworthy, or illegal in your jurisdiction. Advertise here.
1529625916
Hero Member
*
Offline Offline

Posts: 1529625916

View Profile Personal Message (Offline)

Ignore
1529625916
Reply with quote  #2

1529625916
Report to moderator
1529625916
Hero Member
*
Offline Offline

Posts: 1529625916

View Profile Personal Message (Offline)

Ignore
1529625916
Reply with quote  #2

1529625916
Report to moderator
1529625916
Hero Member
*
Offline Offline

Posts: 1529625916

View Profile Personal Message (Offline)

Ignore
1529625916
Reply with quote  #2

1529625916
Report to moderator
Rassah
Legendary
*
Offline Offline

Activity: 1680
Merit: 1001


Academy


View Profile WWW
July 16, 2011, 04:28:20 PM
 #22


I get weird numbers. Can you provide an Open Document Spreadsheet with an example?


I did the calculation with some real numbers and included the output of an excel spreadsheet.


Yep, I get the same numbers.
The only thing that still concerns me though is that the lender needs to get (1+i)*(1+d) return on his investment, yet this calculates each k outstanding balance to be paid off as just Bal*(1+i)...

In your example, the loan interest rate is 5% so the lender only needs to get 5% interest on the balance. It may end up "feeling" closer to 8% interest with respect to purchasing power (i.e. 5% interest plus 3% deflation), but the loan interest rate does not include deflation just like a typical 5% loan from a bank in dollars with 3% inflation is still just a loan for 5% even though the inflation makes it feel more like 2% with respect to purchasing power.

*facepalm* Of course. Deflation growth comes from holding the cash, not from the borrower paying it directly.

im3w1l
Sr. Member
****
Offline Offline

Activity: 280
Merit: 250


View Profile
July 16, 2011, 05:56:41 PM
 #23

You lost me at unbalanced parenthises
Meni Rosenfeld
Donator
Legendary
*
Offline Offline

Activity: 2044
Merit: 1000



View Profile WWW
July 16, 2011, 06:05:47 PM
 #24

...
Something about the x*(1+d)^(-k) formula didn't seem right, either. After a while and a lot of wrangling and testing the algebra, I figured out that, due to this step calculating deflation, it should be -d, and to push the x value into the future instead of the present, the k should be positive. Final formula for that is
...
In copyable plaintext format, the formula is
((1-d)^k P(d+i))/((d-1) (-1+(1+i)^(-n) (1-d)^n))
...
The sad thing is, that is NOT a very pretty formula. But at least it works.
My derivation, as I explained, is based on the assumption that $1 at year 1 is equivalent to $(1+d) at year 0. It looks like you wanted that $1 at year 0 is equivalent to $(1-d) at year 1. So, let R = (1+i)/(1-d), and use the formula P_0*[(R-1)/(1-R^(-n))]*(1-d)^k.

It shouldn't matter too much, because 1/(1-d) = 1 + d + O(d^2).

1EofoZNBhWQ3kxfKnvWkhtMns4AivZArhr   |   Who am I?   |   bitcoin-otc WoT
Bitcoil - Exchange bitcoins for ILS (thread)   |   Israel Bitcoin community homepage (thread)
Analysis of Bitcoin Pooled Mining Reward Systems (thread, summary)  |   PureMining - Infinite-term, deterministic mining bond
Pages: « 1 [2]  All
  Print  
 
Jump to:  

Sponsored by , a Bitcoin-accepting VPN.
Powered by MySQL Powered by PHP Powered by SMF 1.1.19 | SMF © 2006-2009, Simple Machines Valid XHTML 1.0! Valid CSS!