Bitcoin loan payment formula (WARNING: MATHS AHEAD!) [FORMULAS FIXED]

[kwhcoin]

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.

[Rassah]

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]

You lost me at unbalanced parenthises

[Meni Rosenfeld]

...

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).