A simple simulation of loan repayments

loan_repayments_random_search

P0 = c(...)        # initial principal
R = c(...)         # annualized interest
r = (1+R)^(1/12)-1 # monthly interest

np = length(P0)

X = ...  # monthly willingness-to-pay

BB = 1e7 # repetitions
# slightly more principled... find how many months it takes if
#   all loans are combined at the highest interest rate
# PP = sum(P0); rr = max(r)
# optim(20, method='Brent', lower=0, upper=600,
#       function(t) (PP*(1+r)^t - X*t)^2)
JJ = 50L # max payments [could be more general than just guessing...]
sequence = vector('list', BB)

for (ii in seq_along(sequence)) {
  P = P0
  pmts = matrix(0, nrow = JJ, ncol = np) # defaults to 0, useful for once one is paid off
  jj = 1L
  while (jj <= JJ && any(to_pay <- P > 0)) {
    # random search --> uniform random guess of payments
    p = runif(sum(to_pay)) # random payments; normalize to sum to X next
    pmts[jj, to_pay] = X*p/sum(p)
    P = (1+r)*(P - pmts[jj, ])
    while (any(neg_idx <- P < 0) && any(pos_idx <- P > 0)) { # overpayment loop... not 100% sure it's finite
      distr = sum(abs(P[neg_idx]))/sum(pos_idx)
      P[pos_idx] = P[pos_idx] - distr
      P[neg_idx] = 0
    }
    
    jj = jj + 1L
  }
  sequence[[ii]] = pmts[1:(jj-1L), ]
}

table(vapply(sequence, nrow, 1L))