Build a mortgage amortisation schedule

A lender's customer wants to see where their money goes. They are taking a 25-year repayment mortgage of $300,000 at 4.5% a year, paid monthly, and are thinking of paying $200 a month on top.

The lending team needs a schedule it can hand over, and a clear answer to "what does the extra $200 buy me?".

Your task

1. Write monthly_payment(principal, annual_rate, years). The monthly rate is the annual rate divided by 12.
2. Write schedule(principal, annual_rate, years, extra=0.0): one dict per month with the keys month, payment, interest, principal and balance. With an extra payment the loan ends early, and the last payment only clears what is left.
3. Write interest_saved(principal, annual_rate, years, extra).

The data

The loan terms are PRINCIPAL, ANNUAL_RATE and YEARS in the code.

Hint: Where to start

The payment makes the present value of every payment equal the loan. That present value is a finite geometric series, the subject of lesson 1.5.2; lesson 1.5.5 prices a mortgage the same way.

Hint: Building the schedule

Each month, interest is the balance times the monthly rate. The rest of the payment repays principal. Stop when the balance reaches zero.