How to calculate a monthly mortality rate?

Question

If the instantaneous mortality rate for a species (or a group of humans) is 0.1/year, what is the mortality rate per month? Can you just divide $0.1/12$? This seems too simple and incorrect because mortality is an instantaneous rate.

Answer 1

Think of mortality like we think of compound interest: If I said that the effective annual rate of interest of an investment is $10\%$ per year, then what is the equivalent monthly rate of interest? That is to say, $$(1+j)^{12} = 1+i,$$ where $j$ is the monthly interest rate, and $i = 0.10$ is the effective annual rate. This gives us $$j = (1+i)^{1/12} - 1 = (1.1)^{1/12} - 1.$$ The force of mortality works in the same way.