user: The description is rather long but it tries to explain what a financing plan is. 

The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures 
that the loan is paid off in full with interest at the end of its term. 

The monthly payment formula is based on the annuity formula. 
The monthly payment `c` depends upon:

- `rate` - the monthly interest rate is expressed as a decimal, not a percentage. 
The monthly rate is simply the **given** yearly percentage rate divided by 100 and then by 12.

- `term` - the number of monthly payments, called the loan's `term`.
- `principal` - the amount borrowed, known as the loan's principal (or `balance`).

First we have to determine `c`.

We have: `c = n /d` with `n = r * balance` and `d = 1 - (1 + r)**(-term)` where `**` is the `power` function (you can look at the reference below).

The payment `c` is composed of two parts. The first part pays the interest (let us call it `int`)
due for the balance of the given month, the second part repays the balance (let us call this part `princ`) hence for the following month we get a `new balance = old balance - princ` with `c = int + princ`. 

Loans are structured so that the amount of principal returned to the borrower starts out small and increases with each mortgage payment. 
While the mortgage payments in the first years consist primarily of interest payments, the payments in the final years consist primarily of principal repayment.

A mortgage's amortization schedule provides a detailed look at precisely what portion of each mortgage payment is dedicated to each component.

In an example of a $100,000, 30-year mortgage with a rate of 6 percents the amortization schedule consists of 360 monthly payments.
The partial amortization schedule below shows with 2 decimal floats
the balance between principal and interest payments.

--|num_payment|c          |princ      |int        |Balance    |
--|-----------|-----------|-----------|-----------|-----------|
--|1          |599.55     |99.55      |500.00     |99900.45   |
--|...        |599.55     |...        |...        |...        |
--|12         |599.55     |105.16     |494.39     |98,771.99  |
--|...        |599.55     |...        |...        |...        |
--|360        |599.55     |596.57     |2.98       |0.00       |

# Task:
Given parameters 
```
rate: annual rate as percent (don't forgent to divide by 100*12)
bal: original balance (borrowed amount) 
term: number of monthly payments
num_payment: rank of considered month (from 1 to term)
```
the function `amort` will return a formatted string:

`"num_payment %d c %.0f princ %.0f int %.0f balance %.0f" (with arguments num_payment, c, princ, int, balance`)

# Examples:
```
amort(6, 100000, 360, 1) ->
"num_payment 1 c 600 princ 100 int 500 balance 99900"

amort(6, 100000, 360, 12) ->
"num_payment 12 c 600 princ 105 int 494 balance 98772"

```
# Ref

Answer: {"fn_name": "amort", "inputs": [[7.4, 10215, 24, 20], [7.9, 107090, 48, 41], [6.8, 105097, 36, 4], [3.8, 48603, 24, 10], [1.9, 182840, 48, 18], [1.9, 19121, 48, 2], [2.2, 112630, 60, 11], [5.6, 133555, 60, 53], [9.8, 67932, 60, 34], [3.7, 64760, 36, 24], [4.6, 85591, 36, 5], [7.0, 168742, 48, 16], [9.6, 17897, 60, 23], [5.2, 53521, 60, 51], [6.8, 139308, 60, 38], [5.0, 182075, 24, 9], [8.0, 128263, 36, 26], [7.8, 112414, 60, 37], [4.9, 93221, 36, 5], [1.2, 146157, 48, 20], [3.6, 168849, 24, 11], [9.3, 87820, 60, 14], [8.7, 155744, 36, 31], [6.4, 179023, 36, 11], [8.3, 38495, 36, 15], [9.6, 150614, 24, 19], [2.5, 159363, 48, 19], [4.7, 56245, 48, 11], [1.5, 142777, 36, 32], [9.6, 187340, 60, 28], [2.4, 57707, 24, 14], [3.0, 180678, 36, 31], [2.0, 139586, 24, 13], [5.3, 142498, 60, 46], [9.0, 150309, 48, 29], [7.1, 60232, 60, 56], [8.7, 172214, 36, 14], [9.0, 187174, 60, 12], [9.5, 119722, 60, 23], [9.2, 10536, 36, 15], [1.9, 70139, 24, 13], [4.5, 141454, 36, 23], [4.5, 154486, 24, 7], [2.2, 20254, 36, 35], [3.7, 114512, 36, 23], [8.6, 121685, 48, 24], [1.1, 171542, 48, 25], [1.1, 121991, 48, 20], [8.9, 162862, 60, 46], [1.9, 152921, 60, 19]], "outputs": [["num_payment 20 c 459 princ 445 int 14 balance 1809"], ["num_payment 41 c 2609 princ 2476 int 133 balance 17794"], ["num_payment 4 c 3235 princ 2685 int 550 balance 94447"], ["num_payment 10 c 2106 princ 2009 int 98 balance 28799"], ["num_payment 18 c 3959 princ 3769 int 189 balance 115897"], ["num_payment 2 c 414 princ 384 int 30 balance 18353"], ["num_payment 11 c 1984 princ 1810 int 174 balance 92897"], ["num_payment 53 c 2557 princ 2464 int 93 balance 17571"], ["num_payment 34 c 1437 princ 1153 int 283 balance 33532"], ["num_payment 24 c 1903 princ 1829 int 75 balance 22389"], ["num_payment 5 c 2550 princ 2256 int 294 balance 74397"], ["num_payment 16 c 4041 princ 3335 int 706 balance 117641"], ["num_payment 23 c 377 princ 278 int 98 balance 12025"], ["num_payment 51 c 1015 princ 972 int 43 balance 8939"], ["num_payment 38 c 2745 princ 2411 int 335 balance 56634"], ["num_payment 9 c 7988 princ 7474 int 514 balance 115917"], ["num_payment 26 c 4019 princ 3736 int 283 balance 38758"], ["num_payment 37 c 2269 princ 1942 int 327 balance 48320"], ["num_payment 5 c 2790 princ 2449 int 341 balance 81077"], ["num_payment 20 c 3120 princ 3031 int 89 balance 86109"], ["num_payment 11 c 7302 princ 7002 int 300 balance 92965"], ["num_payment 14 c 1836 princ 1277 int 559 balance 70807"], ["num_payment 31 c 4931 princ 4722 int 209 balance 24127"], ["num_payment 11 c 5479 princ 4771 int 708 balance 127911"], ["num_payment 15 c 1212 princ 1041 int 170 balance 23607"], ["num_payment 19 c 6922 princ 6599 int 323 balance 33796"], ["num_payment 19 c 3492 princ 3281 int 211 balance 98178"], ["num_payment 11 c 1288 princ 1110 int 178 balance 44271"], ["num_payment 32 c 4058 princ 4033 int 25 balance 16183"], ["num_payment 28 c 3944 princ 3032 int 912 balance 110949"], ["num_payment 14 c 2465 princ 2411 int 54 balance 24381"], ["num_payment 31 c 5254 princ 5176 int 78 balance 26076"], ["num_payment 13 c 5938 princ 5821 int 117 balance 64670"], ["num_payment 46 c 2709 princ 2535 int 173 balance 36695"], ["num_payment 29 c 3740 princ 3221 int 519 balance 66007"], ["num_payment 56 c 1196 princ 1161 int 35 balance 4712"], ["num_payment 14 c 5452 princ 4618 int 835 balance 110505"], ["num_payment 12 c 3885 princ 2694 int 1191 balance 156135"], ["num_payment 23 c 2514 princ 1863 int 651 balance 80372"], ["num_payment 15 c 336 princ 284 int 52 balance 6495"], ["num_payment 13 c 2981 princ 2925 int 56 balance 32478"], ["num_payment 23 c 4208 princ 3993 int 215 balance 53292"], ["num_payment 7 c 6743 princ 6304 int 439 balance 110852"], ["num_payment 35 c 582 princ 580 int 2 balance 581"], ["num_payment 23 c 3366 princ 3224 int 142 balance 42823"], ["num_payment 24 c 3005 princ 2514 int 491 balance 66044"], ["num_payment 25 c 3655 princ 3575 int 79 balance 83139"], ["num_payment 20 c 2599 princ 2531 int 68 balance 71813"], ["num_payment 46 c 3373 princ 3019 int 354 balance 44694"], ["num_payment 19 c 2674 princ 2502 int 172 balance 106057"]]}