Convertible m-thly

Study guide: Exam FM-2

A Nominal Interest Rate is convertible $m$ -thly (or compounded $m$ times per year) when interest is credited $m$ times per year at the periodic rate $i^{(m)}/m$ . The equivalent effective annual rate is:

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

Common cases: $m=2$ (semi-annual), $m=4$ (quarterly), $m=12$ (monthly), $m=365$ (daily).
As $m \to \infty$ , the nominal rate convertible $m$ -thly approaches continuous compounding and the Force of Interest $\delta = \ln(1+i)$ .

Monthly Rate to Annual Effective Rate A savings account pays a nominal rate of 6% convertible monthly ( $m=12$ ). Find the equivalent effective annual rate.

Answer $1 + i = \left(1 + \frac{0.06}{12}\right)^{12} = (1.005)^{12} = 1.06168$ $i = 6.168\%$