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.
Table A.1 Effect of the Compounding Frequency on the Value of $100 at the End of One Year When the Interest Rate is 10% per Annum
| Compounding | Value of $100 at |
| Frequency | End of Year ($) |
| Annually (m=1) | 110.00 |
| Semiannually (m=2) | 110.25 |
| Quarterly (m=4) | 110.38 |
| Monthly (m=12) | 110.47 |
| Weekly ( ... |
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