Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add JoelLewis/finance_skills --skill time-value-of-moneygit clone --depth 1 https://github.com/JoelLewis/finance_skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/joellewis/finance_skills/time-value-of-money)<a href="https://agentmods.dev/skills/joellewis/finance_skills/time-value-of-money"><img src="https://agentmods.dev/badge/skills/joellewis/finance_skills/time-value-of-money/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/joellewis/finance_skills/time-value-of-money"><img src="https://agentmods.dev/badge/skills/joellewis/finance_skills/time-value-of-money.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- Socket pass
- Snyk pass
- NVIDIA SkillSpector pass
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00192 | $0.02873 |
| Opus 5 | $0.00096 | $0.01437 |
| Sonnet 5 | $0.00038 | $0.00575 |
| Haiku 4.5 | $0.00019 | $0.00287 |
Grade A, and why
time-value-of-money scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 12d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 224 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Time Value of Money
Core Concepts
Future Value (FV)
The value of a present sum after earning interest for n periods at rate r per period.
$$FV = PV \times (1 + r)^n$$
Future value grows exponentially with time, which is the mathematical basis of compound interest.
Present Value (PV)
The current worth of a future sum, discounted back at rate r for n periods. This is the inverse of future value.
$$PV = \frac{FV}{(1 + r)^n}$$
Present value is the cornerstone of all valuation: a dollar today is worth more than a dollar tomorrow because of the opportunity cost of capital.
Compounding Conventions
Interest can compound at different frequencies. The nominal annual rate r_nom compounded m times per year produces different effective yields.
Discrete compounding (m times per year):
$$FV = PV \times \left(1 + \frac{r_{nom}}{m}\right)^{m \times t}$$
Continuous compounding:
$$FV = PV \times e^{r \times t}$$
Effective Annual Rate (EAR):
$$EAR = \left(1 + \frac{r_{nom}}{m}\right)^m - 1$$
For continuous compounding: EAR = e^(r_nom) - 1
Common frequencies:
| Frequency | m |
|---|---|
| Annual | 1 |
| Semi-annual | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
| Continuous | infinity |
Ordinary Annuity
A series of equal payments made at the end of each period for n periods.
Present Value:
$$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$$
Future Value:
$$FV = PMT \times \frac{(1 + r)^n - 1}{r}$$
Annuity Due
A series of equal payments made at the beginning of each period. Each cash flow is one period closer than in an ordinary annuity, so values are scaled by (1 + r).
Present Value:
$$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \times (1 + r)$$
Future Value:
$$FV = PMT \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$
Growing Annuity
A finite series of payments that grow at a constant rate g per period, where g != r.
Present Value:
$$PV = \frac{PMT}{r - g} \times \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right]$$
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 12d ago First seen · 224 lines · 192 tokens per session scan A 2a39444e2e97
time-value-of-money is a skill published in the GitHub repository JoelLewis/finance_skills (184 stars, last pushed 1mo ago), licensed MIT. It adds 192 tokens to every session and 2,873 once invoked, about $0.0010 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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