Compare stated, periodic, and effective rates

Three labels, three questions

For a 6% stated annual rate compounded monthly:

The quote is not the formula input for each month. The monthly rate is not one- year growth. The effective rate is not a new monthly input.

Compute the effective rate

Under the declared convertible quote:

i = j/m = 0.06/12 = 0.005 per month
EAR = (1+i)^m - 1
    = (1.005)^12 - 1
    = 0.0616778119…

At one annual compounding interval, the stated and effective rates are equal. With a positive rate and more than one intra-year interval, effective growth exceeds the stated quote under this convention.

Comparison protocol

EAR aligns only compounding frequency. Before comparing real alternatives, also align:

• cash-flow dates and amount definitions;
• fees, taxes, and transaction costs;
• fixed versus variable terms;
• credit, liquidity, and reinvestment assumptions;
• optionality, penalties, and guarantees; and
• the governing legal disclosure measure.

EAR normalizes one rate convention; it is not an all-in cost, safety measure, or suitability test. A deposit rate and a borrowing rate also belong to different cash-flow directions and decisions even when both use annual percentages.

For example, two fictional loans can have the same rate-based EAR while one charges a $100 origination fee at funding and the other does not. The EAR calculation taught here has aligned compounding but has not aligned net proceeds or total cost; treating the loans as equivalent would therefore outrun the model.

Terminology boundary

“APR,” “nominal,” and “stated” can have product- and jurisdiction-specific definitions. The module explicitly stipulates a quote convertible by simple division. If a real document does not, stop and use its governing convention.

Exit check

Compute the EAR for 12% stated annual interest compounded quarterly: (1.03)^4 - 1 = 12.5509%. Then name two omitted terms that would prevent EAR alone from deciding between actual products.