net premium reserve
When you measure a policy's reserve, you must decide which premium to pretend the policyholder is paying and which costs to count. The simplest, cleanest choice is to ignore expenses entirely and assume the customer pays exactly the net premium. The reserve computed under that idealized assumption is the net premium reserve — the reserve for the benefits alone, as if the policy had no running costs.
Precisely, the net premium reserve at duration t is the present value of future benefits minus the present value of future NET premiums, using the same mortality and interest basis that set the original net premium. Because it deliberately leaves out expenses and uses the equivalence-principle premium, it is a benchmark reserve: clean, consistent, and easy to compute and recurse. For a fully discrete whole-life policy it can be written t-V = A_(x+t) - P * a-double-dot_(x+t), and several equivalent formulas (the 'retrospective' and 'paid-up insurance' forms) give the same number.
The net premium reserve is the textbook foundation and, in many jurisdictions, the basis for the legally required minimum reserve and for cash values. But it is an idealization: it ignores the real expense strain of a new policy, so on a net-premium basis a first-year reserve can look healthier than the policy really is. That gap is exactly why modified reserves (full preliminary term, Zillmer) were invented — they adjust the net premium reserve to acknowledge the heavy first-year acquisition costs.
For a whole-life policy of 1 issued at age x, the net premium reserve at duration 10 is 10-V_x = A_(x+10) - P_x * a-double-dot_(x+10): take the future death benefit's value at the attained age and subtract the value of the remaining net premiums.
The clean benchmark reserve: future benefits minus future net premiums, expenses ignored.
Because it assumes the customer pays the expense-free net premium, the net premium reserve overstates how funded a brand-new policy is — modified reserves correct for first-year expense strain.