ocaml: phase 5.1 mortgage.ml baseline (monthly payment, 200k @ 5% / 30y = $1073)

Standard amortising-mortgage formula:

  payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

where r = annual_rate / 12, n = years * 12.

  let payment principal annual_rate years =
    let r = annual_rate /. 12.0 in
    let n = years * 12 in
    let pow_r = ref 1.0 in
    for _ = 1 to n do pow_r := !pow_r *. (1.0 +. r) done;
    principal *. r *. !pow_r /. (!pow_r -. 1.0)

For 200,000 at 5% over 30 years: monthly payment ~= $1073.64,
int_of_float -> 1073.

Manual (1+r)^n via for-loop instead of Float.pow keeps the program
portable to any environment where pow is restricted.

Tests float arithmetic precedence, for-loop accumulation in a float
ref, int_of_float on the result.

70 baseline programs total — milestone.

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — mortgage.ml baseline (monthly mortgage
+  payment formula, 200k @ 5% / 30y → $1073). Manual `(1+r)^n`
+  computed via for-loop because `Float.pow` may not be available
+  for arbitrary args here. Then plugs into `principal * r *
+  (1+r)^n / ((1+r)^n - 1)`. Tests float arithmetic precedence,
+  for-loop accumulation in a float ref, int_of_float on the result.
+  70 baseline programs total — milestone.
 - 2026-05-09 Phase 5.1 — group_consec.ml baseline (group consecutive
   equals into sublists, 5*10 + 3 = 53). Inner `collect cur acc
   tail` walks while head matches `cur`, accumulates into `acc`,