Pro Tier Module
Compound Interest - Continuous vs Discrete
Continuous vs discrete growth, side by side, with the exact gap and an honest drift signal.
See it run - a worked example, 100% in this browser tab
The problem
Comparing continuous and discrete compounding usually means juggling two formulas, and daily compounding over many years quietly accumulates rounding that no simple calculator flags.
The local-first solution
This plugin evaluates both cited closed forms in exact in-browser f64, quantifies the gap and the effective annual rate, and forms the discrete power by repeated GeoNum multiplication so the drift compartment reports an honest conditioning signal on long schedules. The day-count convention is shown explicitly and nothing is uploaded.
What it does
Discrete balance via the (1 + r/n)^(nt) law at annual, semiannual, quarterly, monthly, or daily frequency
Continuous balance via the e^(rt) limit law
Effective annual rate for the discrete schedule and its continuous equivalent
The exact gap between continuous and discrete growth
Explicit day-count convention (daily uses Actual/365)
GeoNum drift verdict on the repeated-product discrete power
Honest scope
The e^(rt), (1 + r/n)^(nt), and EAR evaluations are the exact f64 results of the cited formulas with no lookup; rate, principal, term, and frequency are all your inputs. Taxes, inflation, fees, contributions or withdrawals, variable or tiered rates, and day-counts other than the simple n-per-year split are not modeled - a nominal rate is not a Regulation Z APR or TISA APY disclosure, and this is not financial advice.
Authorities cited
- Bodie, Z., Kane, A., Marcus, A. (2021). Investments, 12th ed., Ch. 5 - holding-period and effective annual rates; discrete vs continuous compounding (A = P(1 + r/n)^(nt) and A = P e^(rt)).
- Brealey, Myers, Allen (2020). Principles of Corporate Finance, 13th ed., Ch. 2-3 - compound interest, effective annual rate EAR = (1 + r/m)^m - 1, and the continuous-compounding limit e^r.
- Hull, J. C. (2018). Options, Futures, and Other Derivatives, 10th ed., Sec. 4.2 - continuous compounding as the limit of m-per-year compounding; rate conversions e^{R_c} = (1 + R_m/m)^m.
- Goldberg, D. (1991). What Every Computer Scientist Should Know About Floating-Point Arithmetic. ACM Computing Surveys 23(1), 5-48. DOI 10.1145/103162.103163 - rounding error accumulation in repeated products (the conditioning probed here).
- 12 CFR 1030, Appendix A (Truth in Savings Act) - the Annual Percentage Yield (APY) formula APY = 100 * ((1 + interest/principal)^(365/days) - 1); a disclosed-yield analog of the EAR computed here.
- 12 CFR 1026.22 (Regulation Z, Truth in Lending) - APR computation rules; cited to mark the boundary: this tool reports a nominal/effective rate, NOT a Reg Z APR disclosure.
Compare compounding now
Run the comparison in the browser and route results into a Sandbox workspace, a Worklog case, or a Gate client portal. Nothing is uploaded to anyone's cloud.