Force of Interest

Study guide: Exam FM-2

The force of interest \delta is the continuously compounded Interest Rate — the limiting case of a Nominal Interest Rate Convertible m-thly as m \to \infty:

\delta = \ln(1+i)

i = e^\delta - 1

• Under a constant force of interest, the Accumulation Function is:

a(t) = e^{\delta t}

• For a time-varying force \delta(t):

a(t) = \exp\!\left(\int_0^t \delta(s)\,ds\right)

• The force of interest equals the instantaneous rate of change of \ln a(t): \delta(t) = a'(t)/a(t).

Converting Force of Interest to Effective Rate The force of interest is \delta = 0.05 per year. Find the equivalent effective annual rate.

Answer i = e^{0.05} - 1 = 1.05127 - 1 = 5.127\%