Invoice Mathematician in Spain Madrid –Free Word Template Download with AI
Independent Mathematician & Quantitative Consultant
Calle de Serrano 128, 4th Floor, 28006 Madrid, Spain
Tel: +34 91 555 0142 | Email: [email protected]
NIF: 28456789K | Professional Registration: COCM-2019-4471
Bill To (Client)
Empresa Financiera Ibérica S.A.
Attn: Mr. Carlos Mendoza, Head of Quantitative Research
Paseo de la Castellana 259, 28046 Madrid, Spain
CIF: B-85432109
Email: [email protected]
Service Provider
Dr. Alejandro Vega-Ruiz
Mathematician – Specialised in Stochastic Modelling, Numerical Analysis & Applied Probability
Calle de Serrano 128, 4th Floor, 28006 Madrid, Spain
NIF: 28456789K
Bank: Banco Santander – IBAN: ES91 0049 0001 5320 1234 5678
| Ref | Description of Mathematical Services Rendered | Period | Hours | Rate (EUR) | Amount (EUR) |
|---|---|---|---|---|---|
| 01 | Stochastic differential equation modelling for derivative pricing frameworks. Development and validation of Monte Carlo simulation engines for exotic option valuation. Delivered as part of the Q2 2025 quantitative research programme. | Mar 2025 | 48 | 95.00 | 4,560.00 |
| 02 | Numerical optimisation of portfolio risk metrics. Implementation of convex optimisation algorithms for Value-at-Risk and Conditional Value-at-Risk calculations under regulatory constraints (Basel III / CRR). On-site consultation in Madrid office. | Apr 2025 | 36 | 95.00 | 3,420.00 |
| 03 | Applied probability analysis for credit default swap (CDS) correlation structures. Copula-based dependency modelling and sensitivity analysis. Includes written technical report (42 pages) and two presentation sessions for the executive board in Madrid. | May 2025 | 52 | 95.00 | 4,940.00 |
| 04 | Mathematical proof verification and peer review of internal risk model documentation. Formal verification of convergence properties for lattice-based pricing algorithms. Compliance review aligned with ESMA guidelines. | Jun 2025 | 24 | 95.00 | 2,280.00 |
| 05 | Travel and accommodation expenses incurred during on-site engagement at the client's headquarters in Madrid (Calle de Serrano and Paseo de la Castellana locations). Includes intercity rail (AVE) from Barcelona for initial scoping workshop. | Mar–Jun 2025 | — | — | 1,187.50 |
| Subtotal | 16,387.50 |
| VAT (IVA) – 21% (Spanish Value Added Tax) | 3,441.38 |
| Withholding Tax (Retención IRPF) – 15% | (2,458.13) |
| GRAND TOTAL DUE | 17,370.75 |
Notes & Terms of This Invoice
1. This Invoice is issued in accordance with the professional services agreement dated 15 January 2025 between Dr. Alejandro Vega-Ruiz (hereinafter "the Mathematician") and Empresa Financiera Ibérica S.A. (hereinafter "the Client"), both parties being legally established and operating within Spain Madrid.
2. The Mathematician confirms that all mathematical derivations, numerical implementations, and analytical proofs referenced in this Invoice have been conducted to the highest professional standards and are fully documented in the accompanying technical appendices (Appendices A through F, available upon request).
3. Payment of this Invoice shall be made via bank transfer to the IBAN specified above within thirty (30) calendar days from the date of issue. Late payments shall accrue interest at the rate established under Article 20 of the Spanish Late Payment Directive (Ley 3/2004), currently set at the European Central Bank reference rate plus eight percentage points.
4. The 15% withholding tax (retención) has been applied in compliance with the Spanish Personal Income Tax regulations (Ley del IRPF) applicable to professional services rendered by an individual practitioner in Spain Madrid. The Client is responsible for remitting the withheld amount to the Agencia Estatal de Administración Tributaria (AEAT) by the 20th of the month following the month in which the Invoice is settled.
5. All intellectual property, including but not limited to mathematical models, algorithms, proofs, and code generated by the Mathematician in the course of this engagement, shall remain the exclusive property of the Client upon full and final payment of this Invoice, as stipulated in Section 12 of the master services agreement.
6. This Invoice constitutes a legally binding document under Spanish commercial law (Código de Comercio). Any disputes arising from this Invoice shall be subject to the exclusive jurisdiction of the courts of Madrid, Spain.
7. The Mathematician reserves the right to issue a corrective Invoice should any arithmetic or tax calculation error be identified within fifteen (15) business days of the original issue date.
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