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Calculating Quarterly Compounding from a Bank’s Advertised Yield

Article Quant Q&A · Author: james
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Summary

The document explains how to infer a compounding frequency from a quoted nominal annual rate and an effective annual yield. It considers an account advertised at a nominal rate of 9.5% with an annual yield of 9.84%, then applies the quarterly compounding formula: divide the nominal rate by four, add one, raise the result to the fourth power, and subtract one. The resulting effective rate matches the stated annual yield, identifying quarterly compounding.

This is a compact worked example of the relationship between nominal and effective interest rates. The calculation assumes a fixed nominal rate compounded at equal quarterly intervals over one year. It does not discuss fees, changing rates, day-count conventions, or other product terms that could affect an advertised yield, so the method applies to the simplified rate information given.

Key ideas

  • An effective annual yield incorporates the effects of compounding within the year.
  • For quarterly compounding, divide the nominal annual rate by four and compound for four periods.
  • The worked rate conversion matches the stated annual yield and indicates quarterly compounding.
  • The example assumes a constant rate and regular quarterly periods.

Tags

Fixed incomeStatistics
Full text
# Finding the Interest Compounded with Bank Advertising Yield


# Finding the Interest Compounded with Bank Advertising Yield












A bank is advertising 9.5% accounts that yield 9.84% annually. How often is the interest compounded?

Answer is Quarterly.

I've been trying to look for the formula for this; it doesn't seem to be effective rate:

$$ER = (1+i)^m - 1$$

or Nominal Rate

$$i = NR/m$$

What should I be using?

## Answer by Gordon (score 1, accepted)

https://quant.stackexchange.com/a/18555

The quarterly compound rate: \begin{align*} \Big(1+\frac{0.095}{4}\Big)^4 - 1= 9.84\,\%. \end{align*}

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.