Comparing interest: nominal rates, effective rates and compounding
When are two identical interest rates actually comparable?
A rate on its own does not describe an offer. What matters is the balance it applies to, when interest is credited and which other payments are involved. Separating these layers lets you compare deposits and loans without treating different measures as interchangeable.
Three terms with different jobs
The nominal rate is the agreed calculation rate applied to the relevant capital balance. Compounding means that credited interest itself earns interest. An effective annual return summarises the effect of crediting intervals over one year. For consumer loans, the legally defined annual percentage rate is a broader cost measure; section 16 of Germany’s PAngV specifies which costs it includes.
The same nominal rate can produce different annual earnings
Illustrative assumptions: €10,000 is invested for one year at a nominal 5%, without fees or tax. Annual crediting produces €10,500.00. Monthly crediting with immediate reinvestment applies 5% / 12 to the current balance each month: the result is €10,511.62, equivalent to about 5.1162% a year. The extra effect comes from the timing of crediting, not a higher nominal calculation rate.
Payment out is not reinvestment
Someone who withdraws the monthly interest does not receive the assumed compounding benefit. When interest is paid out, you also need to specify the rate at which those payments are invested until the comparison date. A fair comparison uses the same opening amount, duration and treatment of every interim payment.
Handle costs and tax separately
The crediting formula (1 + r / m)^m − 1 uses only the nominal annual rate r and m crediting periods. It is not a complete statutory loan APR calculation. For a loan, actual disbursement and repayment dates and relevant costs belong in the comparison. A modelled return before tax is also not automatically the net income available to spend.
Turn the comparison into a decision
Place amount, fixed-rate period, crediting interval, fees and interim payments side by side. First compare final values under identical assumptions; then assess access to the money and contractual conditions. A small calculated advantage can disappear with a single fee. Future variable rates cannot be predicted this way.
The nominal rate is the calculation rate; compounding is the mechanism. Comparable payment schedules and relevant costs determine a meaningful comparison. A ranking only makes sense after the assumptions match.