Risk Management and Financial Institutions, 4th Edition

APPENDIX A Compounding Frequencies for Interest Rates

Astatement by a bank that the interest rate on one-year deposits is 10% per annum sounds straightforward and unambiguous. In fact, its precise meaning depends on the way the interest rate is measured.

If the interest rate is measured with annual compounding, the bank’s statement that the interest rate is 10% means that $100 grows to

at the end of one year. When the interest rate is measured with semiannual compounding, it means that we earn 5% every six months, with the interest being reinvested. In this case, $100 grows to

at the end of one year. When the interest rate is measured with quarterly compounding, the bank’s statement means that we earn 2.5% every three months, with the interest being reinvested. The $100 then grows to

at the end of one year. Table A.1 shows the effect of increasing the compounding frequency further.

The compounding frequency defines the units in which an interest rate is measured. A rate expressed with one compounding frequency can be converted into an equivalent rate with a different compounding frequency. For example, from Table A.1 we see that 10.25% with annual compounding is equivalent ...