I am little bit confused with actuarial increase in late retirement,
suppose normal retirement is 65 & a employee retires at 67
then as per my logic,
with no pre-retirement mortality : actuarial increase should be (1+i)^2. (since employee's actual retirement is at 67)
with pre-retirement mortality : actuarial increase should be D65/D67

am i right? please guide me.


Thanks

Yes, almost. You have appropriately determined the increased value but need to take it one step further to determine how much to increase the benefit.

Value at age 65 is a₆₅.

Without mortality, increased value is a₆₅ x (1+i)^2. Amount of increase is thus r=a₆₅ x (1+i)^2 / a₆₇. You would multiply benefit at 65 by "r" and not (1+i)^2.

With mortality, increased value is a₆₅ x D₆₅ / D₆₇. Amount of increase is s= {a₆₅ x D₆₅ / D₆₇} / a₆₇ = N₆₅ / N₆₇. You would multiply benefit at 65 by "s" and not D₆₅ / D₆₇.

Thus it follows logically that if Chester Jordan had written California Dreaming, it would have been sung by the N's and the D's rather than the M's and the P's.

In no pre ret mortality, we are giving interest credit to lumpsum till actual retirement and equating to actual ret lumpsum, but a65 cosiders mortality.
and in with pre ret mortality, we use s= {a65 x D65 / D67} / a67 = N65 / N67, but we know the empoyee is alive and the probability that he has survived is 1.

please guide me.

thanks

The issue is whether or not you are increasing for mortality (i.e., we assume so much of you will die, it didn't).

Apart from 415 issues, whether or not to use mortality is often a matter of plan design rather than equity. The equity issue can best be explained by example.

(a) Plan provides death benefit only if married (as mandated by law) but plan covers only cloistered nuns. In short, there is no death benefit so theoretically there is reason to increase for mortality since the benefit is forfeited upon death.

(b) Plan provides actuarially equivalent survivor annuity. In theory, whether live or die, plan pays equivalent value. So, you don't increase for mortality.

Forget what a₆₅ means and look to what happens in deferral period.

Also, the phrase "no pre-ret mortality" may be injecting some confusion. Generally, this refers to the time period between current age and normal retirment date and is (sometimes) part of the actuarial assumptions used for determining liabilities; it also might be part of the definition of actuarial equivalent for the same time period. It does not refer to the time period between NRD and (a later) retirement date.

Does it mean that, we need to consider mortality from NRD to actual (late) retirement date?
if we do in this manner our actuarial increase factor in any case either with pre ret mortality or without pre ret mortality will become N65/N67.