Data Source and Methodology
Primary reference: eCFR, Title 12 — Banks and Banking, Part 1030 (Truth in Savings), Appendix A — Annual Percentage Yield (APY) Formula. Latest version available at: https://www.ecfr.gov/current/title-12/chapter-X/part-1030/appendix-Appendix A to Part 1030.
All calculations in this tool follow the standard compound interest definitions and the APY relationship defined in these regulations. Where users choose “Paid out monthly,” monthly effective rates are derived from APY or the specified nominal/compounding pair.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Glossary of Variables
- P (Principal)
- The initial deposit amount you place in the CD.
- APY
- Annual Percentage Yield (effective annual return including compounding).
- i (Nominal rate)
- Stated annual interest rate without compounding.
- m (Compounding frequency)
- Number of compounding periods per year (1, 2, 4, 12, 365).
- t
- Term in years; t = months / 12.
- M
- Term in months.
- r_m
- Effective monthly rate derived from APY or nominal+compounding.
- A
- Maturity value (principal plus interest).
- I
- Total interest earned over the period.
- τ (tau)
- Marginal tax rate as a decimal (e.g., 0.24 = 24%).
- p
- Penalty months of interest used for early-withdrawal estimate.
How It Works: A Step‑by‑Step Example
Suppose you deposit P = $10,000 at APY = 5.00% for M = 18 months (t = 1.5 years), with reinvestment (compound).
- Compute maturity using APY: A = P × (1 + APY)^t = 10,000 × 1.05^1.5 ≈ $10,759.37.
- Total interest I = A − P ≈ $759.37.
- Annualized return over the term: EAR_term = (A / P)^(1/t) − 1 ≈ 5.00%.
- If interest were paid out monthly instead, use r_m = (1 + 0.05)^(1/12) − 1 ≈ 0.4074% per month; I ≈ 10,000 × 0.004074 × 18 ≈ $733.32; A ≈ $10,733.32.
Frequently Asked Questions (FAQ)
How accurate is this cd calculator?
It applies standard formulas and the APY definition under Truth in Savings. Bank‑specific conventions may vary slightly, which can cause small differences.
Should I enter APY or nominal rate?
If your bank quotes APY, choose APY. If it quotes a nominal rate, select the bank’s compounding frequency to derive the effective yield.
What term length should I choose?
Match the CD’s advertised term. If your plan is to withdraw early, use the advanced early‑withdrawal fields for a penalty estimate.
How is tax handled in this tool?
The tool applies your marginal tax rate to interest to estimate after‑tax results. Taxes vary by jurisdiction and timing; consult a professional for advice.
Can penalties reduce my principal?
Yes, if accrued interest is less than the penalty, some banks deduct the difference from principal. The tool shows a net value that may fall below the initial deposit in such cases.
Does interest paid out monthly compound?
No. If you choose “Paid out monthly,” interest is not reinvested, so the maturity amount is lower than a compounding CD with the same rate and term.
What’s the best compounding frequency?
More frequent compounding yields slightly higher returns. Many banks compound daily. Always use the frequency stated by the bank for accurate estimates.
Formula (LaTeX) + variables + units
\mathrm{APY}=\left(1+\frac{i}{m}\right)^{m}-1
A=P\,(1+\mathrm{APY})^{t}
A=P\left(1+\frac{i}{m}\right)^{m\,t}
r_{m}=(1+\mathrm{APY})^{1/12}-1\quad\text{or}\quad r_{m}=\left(1+\frac{i}{m}\right)^{m/12}-1
I=P \cdot r_{m}\cdot M,\qquad A=P+I
\mathrm{EAR}_{\text{term}}=\left(\frac{A}{P}\right)^{1/t}-1
1) APY from nominal rate and compounding m times per year: $\mathrm{APY}=\left(1+\frac{i}{m}\right)^{m}-1$ 2) Compound growth using APY over t years: $A=P\,(1+\mathrm{APY})^{t}$ 3) Compound growth using nominal i with m compounding periods per year over t years: $A=P\left(1+\frac{i}{m}\right)^{m\,t}$ 4) Effective monthly rate from APY or from nominal/compounding: $r_{m}=(1+\mathrm{APY})^{1/12}-1\quad\text{or}\quad r_{m}=\left(1+\frac{i}{m}\right)^{m/12}-1$ 5) If interest is paid out monthly (no reinvestment), total interest for M months: $I=P \cdot r_{m}\cdot M,\qquad A=P+I$ 6) Effective annualized return over the actual term (t years): $\mathrm{EAR}_{\text{term}}=\left(\frac{A}{P}\right)^{1/t}-1$ 7) After-tax maturity with tax rate τ applied to interest: $A_{\text{after}}=P+(1-\tau)(A-P)$ 8) Early withdrawal penalty estimate with p penalty months: $\text{Penalty}\approx P\cdot r_{m}\cdot p,\qquad A_{\text{net}}=A_{\text{withdraw}}-\text{Penalty}$
- T = property tax (annual or monthly depending on input) (currency)
- https://www.ecfr.gov/current/title-12/chapter-X/part-1030/appendix-Appendix A to Part 1030 — ecfr.gov · Accessed 2026-01-19
https://www.ecfr.gov/current/title-12/chapter-X/part-1030/appendix-Appendix%20A%20to%20Part%201030
Last code update: 2026-01-19
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