Home Mortgage

This listing contains two separate mortgage-related financial programs. The first, “MORTGAGE PAYMENT ANALYSIS,” calculates amortisation schedules for a loan given principal, number of periods, and annual interest rate, printing each period’s payment breakdown to screen and optionally to a printer via LPRINT. The second, “PREPAYMENT,” shows the effect of making extra monthly payments on a mortgage, displaying a table of years remaining, effective interest rate, extra payment per month, and total dollars saved compared to the original repayment schedule. Both programs use a 32-character DIM’d string as a right-justification spacer for formatted numeric output, and both support optional hard-copy output. The amortisation formula uses the standard present-value annuity calculation, with rounding applied via the INT(x*100+0.05)/100 pattern to two decimal places.

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Program Analysis

The listing contains two entirely independent BASIC programs saved back-to-back. The first (lines 10–9999) is a period-by-period amortisation schedule generator named MORTGAGE ANALYSI S. The second (lines 10–9999, restarting) is a prepayment-savings calculator named PREPAYMENT. Both share structural idioms but differ in purpose.

Program 1 – Mortgage Payment Analysis

Program Structure

• Lines 10–30: Initialise counter C, dimension spacer string C$, enter SLOW mode.
• Line 100: Title banner in inverse video.
• Lines 1000–1130: User input phase — principal P, periods L, annual rate R, hard-copy flag Y$, starting period WP.
• Line 1900: Switch to FAST mode for calculation.
• Lines 2000–2070: Compute monthly payment M using the annuity formula.
• Lines 2090–2320: Main amortisation loop over N from 1 to L.
• Lines 3000–3220: GOSUB for LPRINT hard-copy output of one period’s data.
• Lines 3500–3550: GOSUB to format a number string to exactly two decimal places.

Annuity Calculation

The monthly payment is derived by the standard present-value annuity formula. The monthly interest rate is I = R/1200. The compound factor T is built iteratively in a loop rather than using a power function (which is unavailable as a single operator):

1. Lines 2020–2040: T = (1+I)^L computed by repeated multiplication.
2. Line 2050: T = 1 - 1/T, giving the annuity denominator.
3. Line 2060: M = P*I/T.
4. Line 2070: Rounds M to two decimal places using INT(M*100+0.05)/100.

Screen vs. Printer Output

The main loop at line 2185 skips screen output for periods before WP or when hard copy is requested (Y$="Y"). The GOSUB at line 2310 handles printer output and itself returns immediately unless both conditions are met (line 3000). This means screen and printer output are mutually exclusive by design — if Y$="Y", no screen display of individual periods occurs.

String Right-Justification

The 32-character string C$ (initialised by DIM to all spaces) is sliced with C$( TO 18-LEN STR$ N) to pad labels and values to a fixed column width for LPRINT output. This is a compact ZX81 idiom that avoids explicit space-printing loops.

Decimal Formatting Subroutine (Lines 3500–3550)

The subroutine at 3500 ensures a number always prints with exactly two decimal places:

• Re-rounds to two places via INT(100*PP+0.05)/100.
• If the result is a whole number (no decimal part), appends ".00".
• If there is only one decimal digit, appends "0".

Note that the test at line 3530 uses VAL P$=INT VAL P$; because STR$ on a ZX81 never produces a trailing .0 for integers, this correctly detects integer values.

Keypress Pause

Line 2302 uses IF INKEY$<>"" THEN PAUSE 40000 — if any key is held during scrolling output, it triggers a long pause, giving the user time to read the screen. This is a common ZX81 technique since there is no built-in “press any key to continue” facility.

Anomalies and Notes – Program 1

• Line 2110 is REM (empty remark) — it appears to be a vestigial page-break handler stub; the counter C is incremented at 2315 and checked at 2100, but the only action taken is resetting C=0 with no actual page-break output.
• The rounding bias of +0.05 (rather than the standard +0.5) at lines 2070 and 2140 introduces a systematic downward rounding bias for values with three or more decimal places, which may cause the running principal P to drift slightly over a long schedule.
• Line 1110 truncates Y$ to its first character, ensuring only “Y” or “N” is compared later.

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Program 2 – Prepayment Savings Calculator

Program Structure

• Lines 10–50: Optional instructions display, gated by PAUSE 40000 / INKEY$ keypress.
• Lines 60–100: Multi-screen instruction text about prepayment savings.
• Lines 190–299: Input — mortgage amount P, years Y, interest rate R, hard-copy flag via INKEY$.
• Lines 300–379: Column header output to screen or printer.
• Lines 380–640: Outer loop over Q (years remaining, descending); inner loop at 520 simulates one full year.
• Lines 650–730: Summary output, then RUN to restart.
• Lines 1000–1010: GOSUB captures original payment OP.
• Lines 2000–2020: GOSUB formats and LPRINTs one row.
• Lines 3000–3050: GOSUB prints header to printer.

Hard-Copy Input Technique

Lines 294–296 use a polling loop on INKEY$ rather than INPUT to capture the hard-copy flag. This avoids requiring the user to press ENTER after a single keypress, giving a more responsive feel.

Effective Interest Rate Calculation

Lines 582–585 compute a scaled “effective interest rate” IR for display. The interest component of the current payment minus the principal-only portion is computed, then normalised against its value at the original term (ZZ, saved at line 583), and scaled by the nominal rate R. This produces an approximate effective rate column rather than the nominal rate, though the methodology is heuristic rather than actuarially precise.

Extra Payment Column

EM at line 570 is INT((M - OP)*100 + 0.05)/100 — the difference between the current scenario’s payment and the original full-term payment, representing how much extra per month would be needed to pay off in Y years rather than YY years.

Dollars Saved Column

MX (line 510) holds the total cost of the mortgage at the original term. MY = Y*M*12 is the total cost at the current (shorter) term. The column INT(MX-MY) is the gross saving, truncated to whole dollars.

Anomalies and Notes – Program 2

Line	Issue
530	A = INT(P*I*100*100+0.5)/100 — multiplies by 10000 then divides by 100, yielding a value 100× too large for the interest component. This appears to be a bug: the division should be by 10000, or the multiply should be by 100. The result is that A (interest portion) and B (principal portion) in this program are scaled incorrectly, though since only the payment total M is displayed rather than the split, the visible output is unaffected.
591	IF YY-Q>14 THEN PAUSE 10000 — after 14 rows have scrolled, a pause is inserted to prevent the display from scrolling past readable range. This is a pragmatic screen-paging substitute.
570	Uses rounding bias +0.05 instead of +0.5 for two decimal places — same systematic issue as Program 1.
80–90	Long string literals exploit the ZX81’s ability to wrap display across multiple screen lines within a single PRINT statement, producing formatted multi-paragraph text from two lines of BASIC.

Shared Idioms Across Both Programs

• DIM spacer string: Both programs DIM a 32-character string (C$ / Z$) and slice it to generate right-aligned padding for LPRINT columns.
• FAST/SLOW switching: Both switch to FAST mode for computation and SLOW for display, maximising calculation speed while keeping output readable.
• Iterative power: Both compute (1+I)^N via a FOR loop, working around the absence of a general exponentiation function for this use case.
• RUN at line 9999: Both end with RUN to restart after completion, creating a continuous-loop kiosk-style operation.