Nominal and equivalent rates
Core study note
Older business-math terminology aligned to current interest measurement
Nominal quote versus effective growth
A nominal annual rate j^(m) convertible m times per year uses periodic rate j^(m)/m. Its one-year accumulation factor is (1 + j^(m)/m)^m.
An equivalent annual effective rate i therefore satisfies 1 + i = (1 + j^(m)/m)^m.
Why equivalence matters
Two rates are comparable only after they are placed on the same time basis. The lab shows the one-year accumulation side by side rather than treating rate conversion as a memorized substitution.