## Problem Given a loan principal `P`, annual interest rate `r` (as a decimal), and term in months `n`, compute the full amortization schedule - the breakdown of each monthly payment into principal and interest portions. ```python def amortization_schedule( principal: float, annual_rate: float, months: int ) -> List[dict]: # Returns list of {month, payment, principal_paid, interest_paid, remaining_balance} ... ``` **Example:** ``` P=10000, annual_rate=0.06, months=12 Monthly rate = 0.06/12 = 0.005 Monthly payment = P * r / (1 - (1+r)^-n) = 10000 * 0.005 / (1 - 1.005^-12) = 860.66 Month 1: interest = 10000 * 0.005 = 50.00 principal = 860.66 - 50.00 = 810.66 balance = 10000 - 810.66 = 9189.34 ... Month 12: balance rounds to 0.00 ``` ## Follow-ups 1. How do you handle rounding errors so the final balance is exactly $0.00? 2. Extend to support extra monthly payments that reduce the remaining principal. 3. How would you compute the total interest paid and the effective APR if fees are included? 4. Model a variable-rate loan where the interest rate changes every 12 months.

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Payment Schedule - Generate Amortization Schedule for a Loan

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Problem Given a loan principal P, annual interest rate r (as a decimal), and term in months n, compute the full amortization schedule - the breakdown of each monthly payment into principal and interest portions. Example: Follow-ups How do you handle rounding errors so the final balance is exactly $0.00? Extend to support extra monthly payments that reduce the remaining principal. How would you compute the total interest paid and the effective APR if fees are included? Model a variable-rate loan…

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Payment Schedule - Generate Amortization Schedule for a Loan

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