Nominal, periodic, and effective rates

A rate quoted as "6 percent per year" can mean three different things on a CFA Chartered Financial Analyst (CFA) problem: a Stated Annual Rate (SAR) compounded once per year, an SAR compounded m times per year, or an Effective Annual Rate (EAR) that already absorbs the compounding effect. The candidate has to convert between them every time the problem mentions a non-annual compounding frequency.

This page walks four worked rate conversions through the BA II Plus ICONV worksheet and the HP 12C's manual conversion path. The two answers agree to four decimals because both engines share the canonical compounding solver.

Try the BA II Plus calculator

Try the HP 12C calculator

The conversion formulas

For discrete compounding m times per year:

EAR = (1 + SAR / m) ^ m − 1

For continuous compounding:

EAR = e ^ SAR − 1

The inverse forms (solving for SAR given EAR) follow by algebra.

The BA II Plus ICONV worksheet automates the discrete forms. The HP 12C has no built-in equivalent; candidates compute the formula by hand on the stack.

Worked example 1: SAR to EAR (discrete)

Problem. A bank quotes 6 percent compounded monthly. Compute the EAR.

BA II Plus (ICONV worksheet):

1. 2nd then ICONV
2. Cursor on NOM. Type 6. Press ENTER.
3. Arrow down to C/Y. Type 12. Press ENTER.
4. Arrow down to EFF. Press CPT.

Expected EFF: 6.1678 percent.

HP 12C (manual):

In cleaner stack order: 0.06 ENTER 12 ÷ 1 + 12 y^x 1 − 100 ×.

Expected display: 6.1678.

The two paths give the same answer.

Worked example 2: EAR to SAR (discrete)

Problem. A 6.1678 percent EAR. Compute the SAR with monthly compounding.

BA II Plus (ICONV worksheet):

1. 2nd then ICONV
2. Arrow to EFF. Type 6.1678. Press ENTER.
3. Arrow to C/Y. Type 12. Press ENTER.
4. Arrow to NOM. Press CPT.

Expected NOM: 6.0000 percent (to four decimals).

HP 12C (manual): 1.061678 ENTER 12 1/x y^x 1 − 12 × 100 ×.

Expected display: 6.0000.

Worked example 3: continuous compounding SAR to EAR

Problem. A bank quotes 6 percent compounded continuously. Compute the EAR.

The BA II Plus ICONV worksheet does not natively handle continuous compounding. Use the formula directly on either device.

BA II Plus: 0.06 then 2nd then e^x then 1 then - then 100 then ×.

HP 12C: 0.06 g e^x 1 − 100 ×.

Expected EAR: 6.1837 percent.

Note: the BA II Plus second function for e^x sits above the LN key. On the HP 12C, g e^x is the shifted function on the 1/x key.

Worked example 4: EAR to continuous SAR

Problem. A 6.1837 percent EAR is quoted as a continuously compounded rate. Compute the SAR.

SAR = ln(1 + EAR) = ln(1.061837).

BA II Plus: 1.061837 then LN. Multiply by 100 for percent.

HP 12C: 1.061837 g LN. Multiply by 100 for percent.

Expected SAR: 6.0000 percent.

When the conversion matters on the CFA exam

Two recurring contexts:

1. Cross-comparing yields. A money-market quote at 6 percent for 90 days is not directly comparable to a bond yield of 6 percent stated annually. Convert both to EAR before comparing.
2. TVM with a non-annual compounding frequency. A problem stating a 6 percent annual rate compounded quarterly requires a periodic rate of 1.5 percent in the TVM register, with N expressed in quarters. The same problem stated with a 6.1364 percent EAR and asking for a five-year FV is solved at N = 5 and I/Y = 6.1364, treating the rate as the effective annual rate.

Mixing conventions inside a single problem is the most common candidate error in this area.

How Charterly catches conversion mistakes

The Charterly engine treats the rate stored in TVM as the periodic rate for that compute. There is no automatic conversion. The mistake-detection layer does not flag conversion errors today because the calculator alone cannot infer which rate convention the candidate intended. Drill-aware questions that include the rate convention in the seeded inputs will surface a hint when the answer is off by the conversion factor, but the standalone calculator respects whatever the candidate typed.

The cross-device parity holds because both engines compute the discrete and continuous formulas with the same precision (Decimal.js full precision under the hood, displayed to the user's decimal-places setting).

Frequently asked questions

Why does the BA II Plus ICONV worksheet exist if I can compute EAR by hand? For speed and to avoid typos on the exam. ICONV is one keystroke shorter than the formula on most CFA problems. The trade-off is one more setting to remember.

Does the HP 12C have an equivalent of ICONV? Not built in. The HP 12C does the conversion on the stack. The keystroke count is similar; the cognitive load is slightly higher because the candidate has to remember the formula.

Is the periodic rate the same as the effective periodic rate? For TVM purposes on the CFA exam, yes. The periodic rate stored in I/Y is the effective rate over one period.

Does continuous compounding appear on Level I? Continuous compounding appears in the curriculum as a comparison case and in fixed-income for instantaneous forward rates. It is rarer on Level I than on Level II.

Where do I practice conversions like these? Charterly's question library includes Learning Outcome Statement (LOS) tagged drills on rate conversions. Browse the LOS tagged drills.