Nominal Interest Rate Convertible m-thly

Study guide: Exam FM-2

The nominal interest rate convertible m-thly, denoted i^{(m)}, is an annual rate that is compounded m times per year. Each period, interest at rate i^{(m)}/m is credited.

• The relationship to the effective annual rate i is:

\left(1 + \frac{i^{(m)}}{m}\right)^m = 1 + i

i^{(m)} = m\!\left[(1+i)^{1/m} - 1\right]

• As m \to \infty, i^{(m)} \to \delta (the Force of Interest).
• See also: Convertible m-thly and Nominal Discount Rate Convertible m-thly.

Converting Annual to Quarterly Rate The effective annual rate is 8\%. Find the nominal rate convertible quarterly i^{(4)}.

Answer

\begin{align*}
i^{(4)} &= 4\left[(1.08)^{1/4} - 1\right] \\
  &= 4(1.0194265 - 1) \\
  &= 4(0.0194265) \\
  &= 0.077706 = 7.771\%
\end{align*}

Check: (1 + 0.077706/4)^4 = (1.0194265)^4 = 1.08.