# Building a Savings Plan # Let's say you make a monthly deposit (PMT) of $55. # How much will your cash grow every month (n) at a 0.7% interest rate (i)? # Answer: $110.38 including $0.38 of earned interest after the first full month. # Then $166.16 including $1.16 etc., and finally $686.01 including $26.01 after a year. # How much cash will you have in 5 years (60 months)? # Answer: 4083.64 including 783.64. # Run the Program then check the details in the History. # Formula: Amount = PMT X ((1+i)^n - 1) : i. # Source: "TI-57 Making Tracks into Programming.pdf#page=159", p. 8-8 import re from math import * from goto import with_goto # pip install goto-statement @with_goto def main(): global ee, mem, rounding, stack, unit, x label .label_rst # Data Input # Monthly payment (PMT) x = 55 # 55 mem[1] = x # STO 1 (32 0) # Interest rate (i) x = 0.007 # 0.007 mem[2] = x # STO 2 (32 0) # Number of months x = 12 # 12 mem[7] = x # STO 7 (32 0) # Month (n) from 1 to 12 x = 0 # 0 mem[3] = x # STO 3 (32 0) sbr_0() # SBR 0 (61 0) # 60th month x = 59 # 59 mem[3] = x # STO 3 (32 0) sbr_0() # SBR 0 (61 0) return # R/S (81) # Data Processing (33 steps) @with_goto def sbr_0(): global ee, mem, rounding, stack, unit, x label .label_0 # 2nd Lbl 0 (86 0) rounding = 2 # 2nd Fix 2 (48) # Month + 1 x = 1 # 1 mem[3] += x # SUM 3 (34 0) x = mem[3] # RCL 3 (33 0) regx.append(fix(x)) # 2nd Pause (36) # PMT X ((1+i)^n - 1) : i x = mem[1] # RCL 1 (33 0) stack.append(x) # X (55) # ( (43) # ( (43) x = 1 # 1 stack.append(x) # + (75) x = mem[2] # RCL 2 (33 0) y = stack.pop() # ) (44) x = y + x stack.append(x) # y^x (35) x = mem[3] # RCL 3 (33 0) y = stack.pop() # - (65) x = pow(y, x) stack.append(x) x = 1 # 1 y = stack.pop() # ) (44) x = y - x y = stack.pop() # : (45) x = y * x stack.append(x) x = mem[2] # RCL 2 (33 0) y = stack.pop() # = (85) x = y / x regx.append(fix(x)) # 2nd Pause (36) stack.append(x) # - (65) x = mem[1] # RCL 1 (33 0) stack.append(x) # X (55) x = mem[3] # RCL 3 (33 0) y = stack.pop() # = (85) x = y * x y = stack.pop() x = y - x regx.append(fix(x)) # 2nd Pause (36) x = mem[3] # RCL 3 (33 0) # Month lower than number of months? if x < mem[7]: # INV 2nd x>=t (- 76) # Yes, go back to the beginning goto .label_0 # GTO 0 (51 0) # No, stop label .end # INV SBR (- 61) # Internal functions def degrees2dms(degrees): """Convert decimal degrees to degrees, minutes, seconds.""" degrees = float(degrees) is_positive = degrees >= 0 if not is_positive: degrees = -degrees minutes, seconds = divmod(degrees * 3600, 60) degrees, minutes = divmod(minutes, 60) # Internal mantissa has 11 digits on TI-57 seconds = f"{seconds:016.13f}".replace(".", "") dms = f"{int(degrees)}.{int(minutes):02}{seconds}".rstrip("0") if not is_positive: dms = "-" + dms return dms def dms2degrees(dms): """Convert degrees, minutes, seconds to decimal degrees.""" match = re.fullmatch( r"(?P[+-])?(?P[0-9]+)\.?(?P[0-9]{1,2})?(?P[0-9]{1,2})?(?P[0-9]*)", str(dms), ) if match is None: raise Exception(f"Calculator error: invalid DMS angle {dms}") angle = match.groupdict() degrees = float(angle["degrees"]) if angle["minutes"]: if len(angle["minutes"]) == 1: angle["minutes"] += "0" degrees += float(angle["minutes"]) / 60 if angle["seconds"]: if len(angle["seconds"]) == 1: angle["seconds"] += "0" degrees += float(angle["seconds"]) / 3600 if angle["remainder"]: degrees += float("0." + angle["remainder"]) / 3600 if angle["sign"] == "-": degrees = -degrees return degrees def fix(number): """Round a number and/or convert it to the scientific notation.""" global ee, rounding if ee: # The scientific notation is on if rounding is None: # Default to the calculator 7 digit precision number = f"{number:.7E}" # Remove trailing 0s number = re.sub("0+E", "E", number) else: # Round as exponent with the given precision number = f"{number:.{rounding}E}" elif rounding is not None: # Rounding is on number = f"{number:.{rounding}f}" else: # No rounding number = str(number) return number def grd2rad(gradian): """Convert gradian to radian.""" return (gradian / 200) * pi def get_calculator_state(): """Return the calculator sate.""" global ee, error, mem, regx, rounding, stack, unit, x return { "ee": ee, "error": error, "fixed_x": fix(x), "mem": mem, "regx": regx, "rounding": rounding, "stack": stack, "unit": unit, "x": x, } def init_calculator_state(state={}): """Initialize the calculator state. Must be called before running the program, see run(). ee -- Scientific notation (EE) error -- Syntax error etc. mem -- Memories (STO) regx -- History of values displayed before a pause (2nd pause) rounding -- Number of digit after the decimal point (2nd Fix) stack -- Internal memory stack used for computing nested operations unit -- Angle unit (2nd Deg, 2nd Rad, 2nd Grad) x -- Display register or X register """ global ee, error, mem, regx, rounding, stack, unit, x ee = state["ee"] if "ee" in state else False error = state["error"] if "error" in state else None mem = state["mem"] if "mem" in state else [0 for i in range(8)] regx = state["regx"] if "regx" in state else [] rounding = state["rounding"] if "rounding" in state else None stack = state["stack"] if "stack" in state else [] unit = state["unit"] if "unit" in state else "Deg" x = state["x"] if "x" in state else 0 def rad2grd(radian): """Convert radian to gradian.""" return (radian / pi) * 200 def rad2unit(number): """Convert radian to degree or gradian.""" global unit number = float(number) if unit == "Deg": number = degrees(number) elif unit == "Grd": number = rad2grd(number) return number def run_program(): """Run the program (the entry point). The calculator must be initialized beforehand, see init_calculator_state(). """ global error, x try: main() except ZeroDivisionError: x = 9.9999999 except UserWarning: # R/S key pass except Exception as e: error = str(e) def unit2rad(number): """Convert degree or gradian to radian.""" global unit number = float(number) if unit == "Deg": number = radians(number) elif unit == "Grd": number = grd2rad(number) return number # Program execution, uncomment to run the file on its own. # init_calculator_state() # run_program() # calculator_state = get_calculator_state() # print(calculator_state)