An annual percentage rate describes a relationship, not a complete cash amount. The result also depends on the starting amount, the period and the way interest is calculated. This article uses fictional figures for general numerical literacy.
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Calculate a simple-interest example
Suppose a hypothetical starting amount is 1,000 units and a stated simple-interest rate is 5% per year for two years. Ignore fees, taxes, payments and all other changes.
Simple interest uses the original principal throughout: 1,000 × 0.05 × 2 = 100 units. Adding that interest to the starting amount gives 1,100 units at the end of the stated period.
Compare annual compounding
In a separate hypothetical example with 5% interest compounded annually, the first year ends at 1,050 units. The second year's interest is 5% of 1,050, or 52.50 units, producing 1,102.50.
The extra 2.50 arises because the first year's fifty units also enter the second year's interest base. It is not a change in the quoted 5% rate.
Read the full convention before comparing figures
Compounding annually is not the same convention as compounding monthly. A nominal rate, an effective annual rate and a rate for a particular subperiod must be interpreted according to their definitions.
Real documents may also specify timing, charges, variable rates and different treatment of payments. The simplified two-year arithmetic does not determine the value or suitability of any real financial product.
Keep the example separate from a recommendation
A checkable explanation identifies the principal, rate, time basis and calculation rule, then shows the intermediate amount. That lets another reader reproduce the result and see which assumptions drive the difference.
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