import warnings
[docs]
def calculate_contribution(principal, future_value, annual_rate, n_periods):
"""
Calculates the contribution required per period to achieve a specified future value
or pay off a loan, considering the possibility of depositing or withdrawing funds.
Parameters
----------
principal : float
The initial loan amount or investment (present value). For loans, this should be a
negative value (e.g., -1000 for a loan of 1000).
future_value : float
The target future value (amount remaining after n_periods). For loans, this is usually 0.
annual_rate : float
Annual interest rate (as a percentage, e.g., 5 for 5%).
n_periods : int
Total number of periods (e.g., months or years). Must be a positive integer.
Returns
-------
float
The payment amount per period required to reach the specified future value
or pay off the loan. A positive value represents an inflow (e.g., making deposits),
while a negative value represents an outflow (e.g., withdrawals or loan repayments).
Raises
------
ValueError
If any input is invalid, such as non-numeric types or invalid ranges.
Warnings
--------
UserWarning
Warnings for potentially unusual inputs.
Examples
--------
>>> calculate_contribution(principal=0, future_value=10000, annual_rate=5, n_periods=120)
"""
# Input validation
if not isinstance(principal, (int, float)):
raise ValueError("Principal must be a number.")
if not isinstance(future_value, (int, float)):
raise ValueError("Future value must be a number.")
if not isinstance(annual_rate, (int, float)) or annual_rate < -100:
raise ValueError("Annual rate must be a number and greater than or equal to -100%.")
if not isinstance(n_periods, int) or n_periods <= 0:
raise ValueError("Number of periods must be a positive integer.")
# Warnings for unusual inputs
if 0 < annual_rate < 1:
warnings.warn("Annual interest rate is unusually low. Did you mean to input a percentage (e.g., 5 for 5%)?", UserWarning)
if n_periods <= 5:
warnings.warn("Number of periods is unusually low. Did you intend to input months instead of years?", UserWarning)
if annual_rate <= 0:
warnings.warn("Annual interest rate is zero or negative, which is uncommon.", UserWarning)
# Convert annual rate to decimal and adjust for monthly periods
rate_per_period = (annual_rate / 100) / 12 # Assume monthly periods
# Handle zero interest rate case
if rate_per_period == 0:
contribution = (future_value - principal) / n_periods
else:
# Calculate contribution using the financial formula
contribution = (principal * rate_per_period * (1 + rate_per_period) ** n_periods +
future_value * rate_per_period) / ((1 + rate_per_period) ** n_periods - 1)
# Adjust sign based on the relationship between principal and future value
if principal > future_value:
return -abs(contribution) # Withdrawal or repayment (negative contribution)
else:
return abs(contribution) # Deposit or investment (positive contribution)