Lots of contingent annuity questions floating around lately. I thought perhaps I’d post an elementary problem (i.e. net premiums) I encountered years ago. Here it goes:
A man aged 30 pays the net single premium for a whole life insurance for $10,000. Twenty years later, what is the terminal reserve?
Familiar as I was only with the solution formats of a few problems in terminal reserves concerning the net annual premiums of whole life, term and endowment insurance, I was stumped. Several hours, simulations, and analyses later, I came up with an assessment. My assessment back then (using the Commutation columns of the COMMISSIONERS' 1958 STANDARD ORDINARY MORTALITY TABLE FOR MALES at 3%, or at any rate of interest for that matter) was
\(\displaystyle 10,000\frac{{M_{30} }}{{D_{50} }} - \sum\limits_{t = 0}^{19} {10,000\frac{{C_{30 + t} }}{{D_{50} }}}\)
At 3%, this amounted to $5,148.17386350266…
I’m sure Sir TKHunny has a more compact assessment.
A man aged 30 pays the net single premium for a whole life insurance for $10,000. Twenty years later, what is the terminal reserve?
Familiar as I was only with the solution formats of a few problems in terminal reserves concerning the net annual premiums of whole life, term and endowment insurance, I was stumped. Several hours, simulations, and analyses later, I came up with an assessment. My assessment back then (using the Commutation columns of the COMMISSIONERS' 1958 STANDARD ORDINARY MORTALITY TABLE FOR MALES at 3%, or at any rate of interest for that matter) was
\(\displaystyle 10,000\frac{{M_{30} }}{{D_{50} }} - \sum\limits_{t = 0}^{19} {10,000\frac{{C_{30 + t} }}{{D_{50} }}}\)
At 3%, this amounted to $5,148.17386350266…
I’m sure Sir TKHunny has a more compact assessment.
