A statement of truth or a wasted opportunity. Lambda helper functions reluctant to return 2D arrays.

tboulden 

That is quite an achievement; an entire amortisation schedule in a cell.  Rather like the numerical analogue of the ship in a bottle!

It might take me a while to assimilate the implications of this and related initiatives.

tboulden 

Looks impressive! I'll need to see if there's a Python equivalent formulation to get my head around it. Regarding the last line:

=CHOOSE(SEQUENCE(,4),
     INDEX(amort,,1),
     INDEX(amort,,2)-INDEX(amort,,1),
     INDEX(amort,,1)-INDEX(amort,,3),
     INDEX(amort,,3))

This looks fairly readable when placed on separate lines but might sometimes be worth creating a LAMBDA function inline in such cases so as to replace INDEX(amort,,i) as col(i), say.

Another option, given people who use higher order functions would generally be familiar with matrices, might be:

=MMULT(amort,TRANSPOSE({1,0,0;-1,1,0;1,0,-1;0,0,1}))

This is a little less convoluted in terms of application, I think. Using the appropriate functions with SCAN, I get the minimal set of values that encapsulate the changes, then break those changes out into their own columns in the final step.

=LET(
    bal,100000,
    nper,120,
    rate,5%/12,
    pmt_,PMT(rate,nper,-bal),
    array_1,
        MAKEARRAY(nper,3,LAMBDA(i,j,j)   ),
    fxns,
        CHOOSE(array_1,
            LAMBDA(x,x),
            LAMBDA(x,x*(1+rate)),
            LAMBDA(x,x-pmt_)
        ),
    amort,SCAN(bal,fxns,LAMBDA(acc,fn,fn(acc))),
    CHOOSE(SEQUENCE(,4),INDEX(amort,,1),INDEX(amort,,2)-INDEX(amort,,1),INDEX(amort,,1)-INDEX(amort,,3),INDEX(amort,,3))
)

tboulden 

It is one thing to know that Lambda functions are first class citizens of the calculation and can be passed as arguments of other functions, it is another to achieve anything useful with the functionality.  Congratulations.  Presumably it is the MAKEARRAY that allows the formula to return the 2D array of results but following the formula is far from straightforward.  

In connection with your other post, it does sometime seem odd having to create a Lambda function that does no more than the built-in function it implements [for me it might be SUMλ which is simply a restricted version of SUM].  It has yet to cause me grief though and, at present, I find the presence of the λ a useful reminder.

Meanwhile, I have been focussing on simpler problems on this forum.  For example, to unpivot a 2D array

"UNPIVOTλ"
= LAMBDA(grid,
    LET(
      fullList, REDUCE( , grid, APPENDλ),
      SORT(UNIQUE(fullList))
    ))

where APPENDλ is defined by

"APPENDλ"
= LAMBDA(list,value,
    IF(value="", list,
    LET(
      n, COUNTA(list),
      k, SEQUENCE(n+1),
      IF(k<=n, list, value))
  ))

I have actually used REDUCE to run over a 2D array in row-major order to deliver value!

PeterBartholomew1  I've applied this REDUCE/COMPOSE construction to a modified version of your original problem. It's not as readable as the LET construction, but I think it will have applications for manipulations that frequently happen together.