---
title: "Loan Amortization 2068"
id: 55046
type: "computer_media"
slug: "loan-amortization-2068"
url: "http://localhost/computer_media/loan-amortization-2068/"
markdown_url: "http://localhost/computer_media/loan-amortization-2068.md"
published_at: "2024-06-11T13:41:03+00:00"
modified_at: "2026-03-31T14:40:46+00:00"
author: "David Anderson"
featured_image:
  url: "http://localhost/wp-content/uploads/2024/06/SCR-20260330-lvnd.png"
excerpt: "Enter a loan amount, term, and interest rate to get a fully formatted amortization schedule showing payment-by-payment interest, principal, and balance breakdowns."
category:
  - name: "Archived Media"
    slug: "archived-media"
    taxonomy: "category"
    url: "http://localhost/category/archived-media/"
post_tag:
  - name: "Downloadable"
    slug: "downloadable"
    taxonomy: "post_tag"
    url: "http://localhost/tag/downloadable/"
  - name: "TS 2068"
    slug: "ts2068"
    taxonomy: "post_tag"
    url: "http://localhost/tag/ts2068/"
model:
  - name: "Timex/Sinclair 2068"
    slug: "ts-2068"
    taxonomy: "model"
    url: "http://localhost/model/ts-2068/"
indiv:
  - name: "Imre Auersbacher"
    slug: "imre-auersbacher"
    taxonomy: "indiv"
    url: "http://localhost/indiv/imre-auersbacher/"
genre:
  - name: "Finance"
    slug: "finance"
    taxonomy: "genre"
    url: "http://localhost/type/finance/"
media_contents:
  - id: 55036
    title: "TS-2068 Computer Programs"
    type: "computer_media"
    url: "http://localhost/computer_media/ts-2068-computer-programs/"
media_type: "Program"
programmers:
  - name: "Imre Auersbacher"
    slug: "imre-auersbacher"
    taxonomy: "indiv"
    url: "http://localhost/indiv/imre-auersbacher/"
mediadate: "1985"
images:
  - url: "http://localhost/wp-content/uploads/2024/06/SCR-20260330-lvnd.png"
media_type_tags: "Finance"
---

# Loan Amortization 2068

This program computes and displays a complete loan amortization schedule, showing the interest, principal, and remaining balance for each monthly payment period. It accepts three inputs — loan amount, number of periods, and annual interest rate — then applies the standard annuity formula to derive the monthly payment and iterates through each period. Two user-defined functions handle numeric rounding to the nearest cent (`FN a`) and string formatting to ensure consistent two-decimal-place display (`FN a$`). The schedule is printed in a right-justified columnar layout using `TAB` expressions computed from string lengths, and a summary section reports total loan amount, total interest paid, and total payments made.

***

## Program Analysis

### Program Structure

The program is organized into a linear sequence of input, calculation, and output phases, with a single reusable formatting subroutine at line `20`:

1. **Initialization (lines 10–18):** REM headers, function definitions, and variable setup.
2. **Input (lines 25–60):** Prompts for loan amount (`a`), number of periods (`n`), and annual interest rate (`y`), then converts the rate to a monthly decimal.
3. **Payment calculation (line 65):** Derives monthly payment `p` using the annuity formula and total interest `d`.
4. **Amortization loop (lines 80–115):** Iterates from period 1 to `n`, computing balance, interest, and principal for each period.
5. **Summary (lines 120–125):** Prints loan amount, total interest, and total payments.
6. **Formatting subroutine (line 20):** Called via `GO SUB 20` to round `x` and produce a formatted string `c$`.

### Mathematical Approach

The monthly payment is derived at line `65` using the standard present-value annuity formula:

`p = a * (y / (1 - (1+y)^(-n)))`

where `y` is the monthly interest rate (`y/1200` of the annual percentage). The remaining balance at period `z` is computed directly at line `80` using the closed-form expression:

`b = (1+y)^z * (p*(((1+y)^(-z))-1)/y + a)`

This avoids accumulating floating-point errors that would arise from iterative subtraction over many periods. The guard at line `85` clamps near-zero balances to exactly zero.

### User-Defined Functions

| Function | Definition | Purpose |
| --- | --- | --- |
| `FN a(x)` | `INT(c*x+0.5)/c` | Rounds `x` to the nearest cent (uses global `c=100`) |
| `FN a$(x,c$)` | Appends `".00"` or `"0"` as needed | Ensures the string always has two decimal places |

Note that `FN a$` takes a parameter also named `c$`, which shadows the global variable `c$` within the function. The logic `(".00" AND x=INT x)` appends `".00"` when the value is a whole number, and `("0" AND ("0"+c$)(LEN c$)=".")` appends a trailing `"0"` when the string has only one decimal digit — exploiting the Spectrum’s string Boolean idiom where a true condition returns the string and false returns an empty string.

### Formatting Subroutine

Lines `20` is a two-statement subroutine called repeatedly: it rounds the global `x` via `FN a`, then formats the result as a string via `FN a$`, storing it in `c$`. The caller sets `x` before each `GO SUB 20` and reads back `c$` afterward. This pattern is used for `i$`, `p$`, and `b$` (interest, principal, balance strings) in lines `95`–`105`.

### Columnar Output with TAB

Line `110` right-justifies each column by computing the tab stop dynamically:

`TAB (3-LEN STR$ z)`, `TAB (12-LEN i$)`, `TAB (21-LEN p$)`, `TAB (32-LEN b$)`

This ensures that numbers of different widths align on their right edge within fixed column positions, without requiring a fixed-width number format. The separator line at line `75` uses a row of block graphic ▀ characters to draw a visual rule under the column headers.

### Miscellaneous Techniques and Notes

- Line `70` uses `POKE 23692,1` to suppress the `scroll?` prompt, allowing the schedule to scroll uninterrupted regardless of its length.
- The `BEEP 0.07,22` at line `18` provides a short startup sound on initialization.
- Line `100` ends with a bare colon, which is syntactically harmless but slightly untidy.
- Line `130` has a redundant second `STOP` statement; only the first is ever reached.
- The variable `t=23` set at line `35` is used in lines `120`–`125` as the right-edge tab column for the summary section, keeping those values right-aligned at column 23.
- Line `200` saves the program with `LINE 10`, designating line `10` as the auto-start line.

## Source Code

```
   10 REM  Loan Amortization 2068
   12 REM  \* 1984  I. Auersbacher
   14 DEF FN a(x)=INT (c*x+0.5)/c
   16 DEF FN a$(x,c$)=c$+(".00" AND x=INT x)+("0" AND ("0"+c$)(LEN c$)=".")
   18 BORDER 5: LET c=100: LET x=0: BEEP 0.07,22: CLS : GO TO 25
   20 LET x=FN a(x): LET c$=FN a$(x,STR$ x): RETURN 
   25 PRINT PAPER 6;"** Loan Amortization Schedule **": PRINT 
   30 PRINT "Loan Amount : $";
   35 INPUT a: PRINT a: LET t=23
   40 PRINT "No. Periods :  ";
   45 INPUT n: PRINT n;" months"
   50 PRINT "Interest (%):  ";
   55 INPUT y: PRINT y
   60 LET y=y/1200: PRINT 
   65 LET p=a*(y/(1-(1+y)^(-n))): LET x=p: GO SUB 20: LET d=n*p-a
   70 PRINT "Monthly Pymt= $";c$: POKE 23692,1: PRINT : LET l=a
   75 PRINT "Pmt Interest  Principal  Balance": PRINT "\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''\''"
   80 FOR z=1 TO n: LET k=(1+y)^(-z): LET b=1/k*(p*(k-1)/y+a)
   85 IF b<0.001 THEN LET b=0
   90 LET i=b-l+p: LET r=p-i
   95 LET l=b: LET x=i: GO SUB 20
  100 LET i$=c$: LET x=r: GO SUB 20: LET p$=c$: LET x=b:
  105 GO SUB 20: LET b$=c$
  110 PRINT TAB (3-LEN STR$ z);z;TAB (12-LEN i$);i$;TAB (21-LEN p$);p$;TAB (32-LEN b$);b$
  115 NEXT z: PRINT : PRINT 
  120 LET x=a: GO SUB 20: PRINT "Loan Amount =";TAB t-LEN c$;c$
  125 LET x=d: GO SUB 20: PRINT "Tot.Interest=";TAB t-LEN c$;c$: LET x=n*p: GO SUB 20: PRINT "Total paymts=";TAB t-LEN c$;c$
  130 STOP : STOP 
  200 SAVE "loans" LINE 10
```