gross (expense-loaded) premium

The net premium pays for the death benefit and nothing else — but a real insurer also has to pay the agent's commission, print the policy, run computers, pay staff and taxes, and earn a profit for its owners. The gross premium is the price actually charged on the contract: the net premium plus enough extra to cover all those running costs and a margin. It is the number on your bill, not the bare cost of the risk.

Precisely, the gross premium G is found by an extended equivalence principle: at issue, the present value of the gross premiums equals the present value of benefits PLUS the present value of expenses (and any required profit margin). In words, G must cover three things — the benefits (the net-premium part), the expenses, and a loading. Expenses themselves come in flavors: big one-time acquisition costs at the start (commission, underwriting), and smaller ongoing costs each year (administration, collecting premiums), plus per-claim settlement costs. Solving the balance for G gives a number larger than the net premium; the gap is the 'expense loading'.

Gross premiums are what determine whether a product is competitive and whether the company makes money. Because the heavy acquisition costs hit in year one but are recovered slowly over the life of the policy, a fresh policy is initially unprofitable — the source of deferred acquisition costs and new-business strain. A caution: the split between 'net' and 'loading' is a modelling convention, not a separate bank account; the policyholder simply pays one gross premium and trusts the insurer's pricing to be adequate without being excessive.