Interest Rates: Nominal, Effective, Real and Period Conversion

The nominal rate is the one stated in the contract or in the advertisement for a financial product. A CD may offer '14.4% per year'. That is the nominal rate. The effective rate is the return you actually earn, taking into account the compounding frequency.

It is common for a rate to be expressed on an annual basis while compounding occurs monthly. When a contract states '14.4% per year compounded monthly', the nominal annual rate is 14.4%, but the monthly rate applied in calculations is 14.4% ÷ 12 = 1.2% per month. That monthly rate of 1.2%, compounded over 12 months, results in an effective annual rate of (1.012)^12 − 1 ≈ 15.39% per year.

The difference between 14.4% (nominal) and 15.39% (effective) may seem small, but on large amounts or over long periods it represents a significant gap. Therefore, when comparing financial products, always convert to the same basis — preferably the effective rate.

Under simple capitalisation (simple interest), rates are proportional: a rate of 12% per year equals 1% per month (divide by 12). Under compound capitalisation (compound interest), the conversion is different — rates are equivalent, not proportional.

To convert an annual rate to an equivalent monthly rate under compound interest, use: r_monthly = (1 + r_annual)^(1/12) − 1. Example: annual rate of 12% → r_monthly = (1.12)^(1/12) − 1 ≈ 0.9489% per month. Note that the proportional rate would be 1%, but the equivalent rate is 0.9489% — a lower result, because compound capitalisation 'works for you' over time.

Likewise, to convert a monthly rate to an equivalent annual rate: r_annual = (1 + r_monthly)^12 − 1. If the monthly rate is 1.5%: r_annual = (1.015)^12 − 1 ≈ 19.56% per year. This means a loan at 'just' 1.5% per month costs nearly 20% per year in effective terms.

The nominal rate of an investment includes two components: the real return (the gain in purchasing power) and the compensation for inflation. The real rate is the return after stripping out inflation. It indicates whether the investment genuinely increased your purchasing power.

The correct formula is the Fisher equation: (1 + r_real) = (1 + r_nominal) ÷ (1 + inflation). Example: a CD earns 10% per year and inflation was 6% per year. Real rate = (1.10) ÷ (1.06) − 1 ≈ 3.77% per year. A simpler (but less precise) approximation is r_real ≈ r_nominal − inflation = 10% − 6% = 4%. The exact formula gives a slightly lower value.

When inflation exceeds the nominal rate, the real rate turns negative — you lose purchasing power even though you are earning money in nominal terms. This is common during periods of high inflation when conservative investments earn below the rate of inflation.

To compare CDs, tax-exempt bonds, Treasury securities, savings accounts and other investments, convert everything to the same basis: effective annual rate after income tax (where applicable). Some bond types are tax-exempt; CDs and Treasury securities have a declining tax schedule (ranging from approximately 22.5% down to 15% depending on the holding period).

Another important reference point is the benchmark. Many CDs are expressed as a percentage of a reference rate — for example, '110% of the overnight rate'. If the overnight rate is 10.5% per year, the CD yields 11.55% per year. To compare with a savings account, check the current rules: when the policy rate is above a certain threshold, the savings account typically yields less than many CDs.

When borrowing, the reverse reasoning applies. A revolving credit card balance can charge 15% per month or more. Converting to an annual rate: (1.15)^12 − 1 ≈ 435% per year. That number alone explains why revolving credit card debt must be avoided at all costs.