FM: Nominal, effective and force-of-interest rates are not interchangeable
The compounding convention belongs to the rate. Convert the rate to the period of your cash flows before using an annuity or accumulation formula. Using an annual nominal percentage as an annual effective percentage silently changes the result.
Worked example or practice scenario
A nominal annual rate of 12% convertible monthly has monthly rate 1% and annual effective rate (1.01)^12−1 ≈ 12.6825%. A constant force of .12 gives annual effective rate e^.12−1 ≈ 12.7497%, a different contract.
Try this next
Find the force equivalent to 12% nominal convertible monthly: 12 ln(1.01). Verify that accumulating 1 for a year under either equivalent description gives the same amount. Keep rates and durations in consistent units.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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