Converting force of interest

Question

If you have a force of interest (delta) which is expressed biannually and is non-constant, is there a way in which I can express this annually? E.g first half year, delta = 0.05 and second half year, delta= 0.07 then the annual delta value would be?

Answer 1

The "average" interest rate for the two periods (as long as they are of equal length) is the solution $r$ to the equation $$ (1.05)(1.07) = (1+r)^2 $$ since these are the factors you multiply the principal by.

The answer is $$ r = 0.05995282914 $$ or just a tiny fraction less than the $6\%$ you'd get by just averaging the interest rates.

If $5$ and $7$ percent rates are themselves annual then your equation is $$ (1.025)(1.035) = (1+r/2)^2 $$ and the solution is $$ r = 0.05997572801 $$ (not very different).