Invoice Mathematician in Germany Frankfurt –Free Word Template Download with AI
Mathematician Consulting & Analytical Services
From (Service Provider)
Dr. Heinrich Vogel, Mathematician
Vogel Analytical Mathematics GmbH
Bockenheimer Landstraße 142
60323 Frankfurt am Main, Germany
Phone: +49 69 5550 8821
Email: [email protected]
VAT ID (USt-IdNr.): DE 318 442 907
HRB: Frankfurt am Main HRB 98 442
Bill To (Client)
Frankfurt Financial Analytics AG
Attn: Dr. Sabine Krüger, CFO
Opernplatz 18
60313 Frankfurt am Main, Germany
Phone: +49 69 7788 4400
Email: [email protected]
VAT ID (USt-IdNr.): DE 294 118 553
Description of Services Rendered
This Invoice is issued by Dr. Heinrich Vogel, a certified Mathematician operating under Vogel Analytical Mathematics GmbH, registered in Germany Frankfurt, in accordance with the professional services agreement dated 01 March 2025. The Mathematician has provided advanced quantitative modelling, stochastic analysis, and algorithmic optimisation services to Frankfurt Financial Analytics AG for the billing period of 01 April 2025 through 31 May 2025. All mathematical computations, derivations, and analytical frameworks were developed and delivered in compliance with the German Commercial Code (Handelsgesetzbuch) and applicable professional standards for mathematical consultancy in Germany Frankfurt.
| Ref. | Service Description | Hours | Rate (EUR) | Amount (EUR) |
|---|---|---|---|---|
| 01 | Advanced stochastic modelling for derivative pricing frameworks; Mathematician-led derivation of PDE solutions and Monte Carlo simulation design | 48 | 185.00 | 8,880.00 |
| 02 | Algorithmic optimisation of portfolio risk metrics; Mathematician consultation on convex optimisation and Lagrangian duality methods | 32 | 185.00 | 5,920.00 |
| 03 | Mathematical proof verification and peer review of internal quantitative research papers; Mathematician expertise in measure-theoretic probability | 20 | 210.00 | 4,200.00 |
| 04 | Workshop delivery: "Applied Functional Analysis for Financial Engineers" – Mathematician-led two-day training session held in Germany Frankfurt | 16 | 250.00 | 4,000.00 |
| 05 | Development of custom numerical integration algorithms; Mathematician supervision of code implementation and validation testing | 24 | 185.00 | 4,440.00 |
| 06 | Ad-hoc mathematical advisory and correspondence; Mathematician availability for urgent analytical queries during the billing period | 10 | 160.00 | 1,600.00 |
| Subtotal (Net) | 29,040.00 EUR |
| VAT (Umsatzsteuer) 19% | 5,517.60 EUR |
| Grand Total (Brutto) | 34,557.60 EUR |
VAT is charged in accordance with § 14 UStG. This Invoice is valid for the billing period 01.04.2025 – 31.05.2025.
Bank Details (Germany Frankfurt) Bank: Deutsche Kreditbank AGIBAN: DE89 2005 0550 1015 7520 88
BIC/SWIFT: DEKXDEFF
Reference: INV-2025-FRA-0047 Payment Method SEPA Direct Debit / Bank Transfer
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Important Notes & Terms
1. This Invoice constitutes a legally binding document under German commercial law. The Mathematician, Dr. Heinrich Vogel, warrants that all mathematical analyses, proofs, and computational results delivered under this engagement are accurate to the best of professional standards and free from intellectual property infringement.
2. Payment is due within thirty (30) calendar days of the issue date of this Invoice. In the event of late payment, statutory interest of 8 percentage points above the European Central Bank base rate shall apply in accordance with § 288 BGB, as is standard practice for commercial transactions in Germany Frankfurt.
3. All deliverables, including mathematical proofs, algorithmic code, and analytical reports, remain the intellectual property of the Mathematician until full payment of this Invoice has been received and confirmed in writing by Vogel Analytical Mathematics GmbH.
4. This Invoice is subject to the jurisdiction of the competent courts in Frankfurt am Main, Germany. Any disputes arising from this Invoice or the underlying services agreement shall be resolved in accordance with the laws of the Federal Republic of Germany.
5. The client acknowledges that the Mathematician has fulfilled all obligations under the professional services agreement for the stated billing period. No further claims or adjustments shall be made for services rendered prior to the issue date of this Invoice.
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