Investment Growth

This program calculates the compound annual growth rate (CAGR) of an investment given a beginning amount, an ending amount, and a number of years. The core formula at line 100 uses the nth-root exponentiation `(E/B)**(1/N)` to derive the periodic rate, which is then rounded to two decimal places via the `INT((I*10000)+.5)/100` idiom at line 110. The program branches at line 130 to display either “POSITIVE GROWTH” or “NEGATIVE GROWTH” with the corresponding percentage change, and a shared GOSUB subroutine at line 400 prints the common summary fields. A loop at lines 280–300 allows repeated calculations without restarting.

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Program Analysis

Program Structure

The program is organized into three logical regions:

1. Input phase (lines 10–81): Prompts the user for beginning amount (B), ending amount (E), and number of years (N), echoing each entered value immediately after input.
2. Calculation and output phase (lines 90–270): Computes the compound annual growth rate, determines sign, and prints the appropriate result block via a shared subroutine.
3. Loop / exit (lines 270–310): Asks whether to run another calculation; a “Y” response branches back to line 20, skipping the initial title print at line 10.

The subroutine at lines 400–440 prints the four summary fields (beginning amount, ending amount, absolute change, and years) and is called from both the positive-growth path (line 150) and the negative-growth path (line 220), avoiding code duplication.

Core Formula

Line 100 computes the compound annual growth rate using the standard CAGR formula:

I = ((E/B)**(1/N)) - 1

The ** operator raises E/B to the power 1/N, equivalent to taking the Nth root of the total return ratio. The result is the per-period rate as a decimal (e.g., 0.05 for 5%).

Rounding Technique

Line 110 applies the classic two-decimal-place rounding idiom:

I = INT((I * 10000) + 0.5) / 100

Multiplying by 10000 and dividing by 100 shifts the value so that rounding to the nearest integer (via adding 0.5 before truncation) gives a result accurate to two decimal places expressed as a percentage. Note that this converts the decimal fraction directly to a percentage figure — for example, 0.0523 becomes 5.23.

Sign-Based Branching

Line 130 tests whether I is negative and routes to line 210 for the decline branch. The positive branch falls through to line 140. Both branches call the shared subroutine and then print the rate label (PC INCREASE or PC DECLINE) with the value of I. Control then converges at line 270 for the repeat-prompt logic.

Variable Summary

Variable	Purpose
B	Beginning (initial) investment amount
E	Ending investment amount
N	Number of years
I	Calculated CAGR (as a percentage after rounding)
C	Absolute change (E - B)
Q$	User response for repeat loop (“Y” or “N”)

Notable Techniques and Idioms

• The repeat loop branches back to line 20 rather than line 10, so the “INVESTMENT GROWTH” title is printed only once per program run.
• Each INPUT statement is immediately followed by a PRINT of the entered variable (lines 41, 61, 81), providing confirmation of the entered value — a common pattern when input is not automatically echoed visibly.
• STOP at line 500 is used as a clean program terminator on the “N” path, with lines 510–520 following as utility lines for saving and re-running.

Potential Anomalies

• If B is entered as zero, line 100 will cause a division-by-zero error (E/B). No input validation is present.
• If N is zero, the expression 1/N also produces a division-by-zero error.
• When I is negative and the rounding at line 110 is applied, the INT(...+0.5) rounding method does not round symmetrically for negative numbers (it rounds toward negative infinity rather than away from zero), so negative rates may be off by one unit in the last digit.
• The label printed for a negative rate is PC DECLINE followed by the already-negative value of I, so the sign is implicit in both the label and the number — users must interpret the negative sign themselves.