Mortgage amortization with extra monthly payments and lump sums

# Mortgage amortization with extra monthly payments and lump sums `input.json` describes a fixed-rate loan plus planned prepayments (synthetic). Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` produces the payment, the baseline payoff, and the full schedule with prepayments. We re-run it on fresh inputs, so do not hard-code anything. ## Input `principal`, `annual_rate` (percent, e.g. 6.125), `years`, `extra_monthly`, `extra_start_month` (first month the extra is paid; months count from 1), `lump_sums` (list of `{"month", "amount"}`; several can fall in the same month and then add up). ## Rules 1. Money is exact cents with `decimal.Decimal` and ROUND_HALF_UP to 0.01 (convert input numbers with `Decimal(str(x))`). 2. Scheduled payment: with float r = annual_rate / 1200 and n = years * 12, x = principal * r / (1 - (1 + r) ** -n) computed in floats; payment = `Decimal(str(x))` rounded to cents. 3. Each month m: interest = round(balance * annual_rate / 1200) (in Decimal). Prepayment = extra_monthly if m >= extra_start_month (else 0) plus the lump sums for month m. If payment + prepayment >= balance + interest, this is the last month: the amount paid is balance + interest and the balance becomes 0. Otherwise the amount paid is payment + prepayment and the balance drops by (amount paid - interest). 4. The baseline is the same loan with no extra and no lump sums. 5. `interest_saved` = baseline total interest - total interest with prepayments; `months_saved` = baseline months - months with prepayments. ## Output `answer.json`: ``` {"payment": ..., "baseline": {"months": ..., "total_interest": ..., "last_payment": ...}, "with_extra": {"months": ..., "total_interest": ..., "schedule": [[month, amount_paid, interest, principal_paid, balance_after], ...]}, "interest_saved": ..., "months_saved": ...} ``` One schedule row per month, money as numbers with 2 decimals. ## Chart (required visual) Also write `chart.svg` in the working directory: a static, self-contained SVG (root element `<svg>`, no scripts, no external images, fonts, stylesheets or links) that can be rendered headless. It must contain `<polyline id="balance">` drawing the with-extra remaining balance by month. ## Scoring The `chart_svg_static` check (one more check, counted in partial credit) passes only if `chart.svg` exists after the fixture run, parses, has root `<svg>`, contains the ids above with the stated tags, and has no `<script>`, `<img>`/`<image>`, `<link>`, `<iframe>`/`<object>`/`<embed>`, `on*` handlers, or `href`/`src` pointing anywhere except `#...` or `data:`. Its drawing is not graded. Hidden checks (partial credit = fraction passed; all must pass), money within 0.011, counts exact: `payment`, `baseline`, `schedule_rows` (every row), `savings` on the given input; `fresh_run_1`, `fresh_run_2` (the whole answer on fresh inputs; one has two lump sums in the same month). Each run has a 60-second limit.