Increasing Death Benefit Mechanics

How the Increasing Death Benefit Works

A universal life policy can define its death benefit as a specified amount plus the policy account value. Under this increasing-benefit option, a larger account value means a larger total amount is paid at death. That does not mean the insurer’s exposure beyond the account value has also increased: the account value is part of the benefit itself.

The calculation must use the account value at the relevant claim time, after applying any account transactions that the contract says occur before that time. This tutorial assumes the policy is in force and focuses on the increasing-benefit formula. It does not add other contractual adjustments.

Definition: Let $S$ be the policy’s specified amount and let $A(t)$ be its account value at time $t$. Under an increasing death benefit option that adds account value to the specified amount, the death benefit at time $t$ is $B(t)=S+A(t)$. The net amount at risk is the death benefit less the account value: $N(t)=B(t)-A(t)$.

These are distinct quantities. The death benefit is the total amount payable under the stated option. The net amount at risk is the portion of that benefit in excess of the account value. The account projection methods covered in the earlier material on universal life cash flows determine $A(t)$; once it is known, the increasing-benefit calculation is direct.

Why the Net Amount at Risk Stays Level

Substitute the increasing-benefit formula into the definition of net amount at risk:

$$ N(t)=B(t)-A(t)=[S+A(t)]-A(t)=S. $$

The account value cancels because it is included in the benefit and then excluded when measuring the net amount at risk. Thus, while the account value and total death benefit can change over time, their difference is the specified amount under this option. This conclusion assumes the stated benefit formula applies at the time being considered.

The result is useful as a consistency check. If an increasing-benefit calculation produces a net amount at risk different from $S$, check whether the account value was included once in the death benefit and subtracted once in the net amount at risk. Also check that both calculations use the account value at the same time.

Worked Example: Benefit and Net Amount at Risk at Death

A hypothetical policy has a specified amount of $175,000. Immediately before a claim is calculated, its account value is $28,450. The increasing-benefit provision adds that account value to the specified amount. Find the death benefit and net amount at risk.

Assumptions. The account value is already established at the claim time, so no further interest or charges are applied. For context, suppose the insured has an annual death probability of $q=0.015$, with deaths distributed uniformly within the year. The requested calculation is conditional on death at this time, so the mortality assumption does not affect the benefit amount. Account value is treated as deterministic for this calculation.

Method. Apply the increasing-benefit formula, then subtract the account value to find the net amount at risk.

Death benefit:

$$ B=175{,}000+28{,}450=203{,}450. $$

Net amount at risk:

$$ N=203{,}450-28{,}450=175{,}000. $$

The death benefit is $203,450, and the net amount at risk is $175,000, equal to the specified amount. As a check, increasing the account value by $10,000 while holding the specified amount fixed would increase the death benefit by $10,000, but would leave the net amount at risk at $175,000.

Common mistake avoided: Calling the death benefit itself the net amount at risk would give $203,450. The correction is to subtract the account value: $203,450 − $28,450 = $175,000.

Project the Account Before Applying the Benefit Formula

The increasing-benefit formula does not determine the account value. That value must first be projected using the contract’s transaction order. In the example below, a net premium allocation is added at the start of each month, interest is credited to the resulting balance, and charges are deducted at month-end. Changing that order can change the account value and therefore the death benefit.

Worked Example: Three-Month Account Projection

A hypothetical policy has a $200,000 specified amount and an opening account value of $36,000. For each of the next three months, a $500 net premium allocation is added at the beginning of the month. The monthly credited interest rate is 0.4%, and a combined $170 in policy charges is deducted at the end of each month. Find the account value, death benefit, and net amount at risk at the end of month 3.

Assumptions. The monthly crediting rate is deterministic; its equivalent effective annual rate is $(1.004)^{12}-1$, approximately 4.91%. For mortality context, assume an annual death probability of $q=0.012$ with deaths uniformly distributed within the year. The claim is stipulated to occur at the end of month 3, so no probability weighting is needed to calculate its amount. The $170 monthly charge is given; it is not recalculated from the mortality assumption.

Method. For each month, add the allocation, credit interest, and then deduct the charge. In symbols, if $A_{j-1}$ is the account value at the prior month-end, then

A_j=(A_{j-1}+500)(1.004)-170.

Month 1:

A_1=(36{,}000+500)(1.004)-170 =36{,}500(1.004)-170 =36{,}646-170 =36{,}476.

Month 2:

A_2=(36{,}476+500)(1.004)-170 =36{,}976(1.004)-170 =37{,}123.904-170 =36{,}953.904.

Month 3:

A_3=(36{,}953.904+500)(1.004)-170 =37{,}453.904(1.004)-170 =37{,}603.719616-170 =37{,}433.719616.

Rounded to the nearest cent, the month-3 account value is $37,433.72. The death benefit is

B_3=200{,}000+37{,}433.719616 =237{,}433.719616 \approx \$237{,}433.72.

The net amount at risk is

N_3=237{,}433.719616-37{,}433.719616 =200{,}000.

Thus the rounded death benefit is $237,433.72, and the net amount at risk is $200,000. The unrounded account value was retained through the benefit calculation; rounding only at the end gives a consistent result.

Common mistake avoided: Crediting interest to the prior balance before adding the premium would use a different transaction order. Here the premium is added first, so month 1 interest is $0.004(36{,}500)=146$, not $0.004(36{,}000)=144$.

Tracking Benefits Across Policy Years

When account values are given at several possible claim dates, calculate the benefit at each date using the corresponding account value. If mortality probabilities are also supplied, keep two tasks separate: first calculate each possible death benefit, then weight those benefits by the probability of death in each period. A conditional death probability for a later year applies only to policies that survived to the start of that year.

Worked Example: Expected Present Value of Claims Over Three Years

A hypothetical policy has a specified amount of $100,000. The account values at the ends of policy years 1, 2, and 3 are projected to be $8,000, $15,000, and $24,000, respectively. The conditional probabilities of death during those years are $q_1=0.01$, $q_2=0.02$, and $q_3=0.03$. Find the expected present value of death claims per policy issued, using an effective annual interest rate of 4%.

Assumptions. The account values and credited interest are deterministic. Mortality follows the stated discrete annual probabilities, conditional on survival to the start of each year. A claim for death during a year is paid at that year-end using that year’s stated account value. No claim is included after year 3. This annual payment-timing assumption is part of the hypothetical calculation.

Method. First calculate the death benefit in each year. Then calculate each unconditional probability of death by multiplying the probability of surviving earlier years by the current year’s conditional death probability.

The benefits are:

B_1=100{,}000+8{,}000=108{,}000,\quad B_2=100{,}000+15{,}000=115{,}000,\quad B_3=100{,}000+24{,}000=124{,}000.

The unconditional death probabilities are:

P(\text{death in year 1})=0.01, $$ $$ P(\text{death in year 2})=(1-0.01)(0.02)=0.99(0.02)=0.0198, $$ $$ P(\text{death in year 3})=(1-0.01)(1-0.02)(0.03) =0.99(0.98)(0.03)=0.029106.

Discount each year-end claim at 4%. With $v=1/1.04$, the expected present value is

108{,}000(0.01)v +115{,}000(0.0198)v^2 +124{,}000(0.029106)v^3.

The three undiscounted probability-weighted claim amounts are $1{,}080$, $2{,}277$, and $3{,}609.144$. Their discounted values are:

\frac{1{,}080}{1.04}=1{,}038.461538\ldots,\quad \frac{2{,}277}{1.04^2}=2{,}105.214497\ldots,\quad \frac{3{,}609.144}{1.04^3}=3{,}208.5159\ldots.

Adding the terms gives $6{,}352.1919\ldots$, so the expected present value is $6,352.19 per policy issued, rounded to the nearest cent. As a check on the benefit mechanics, the net amount at risk in each year is the corresponding benefit less account value: $108{,}000-8{,}000=100{,}000$, $115{,}000-15{,}000=100{,}000$, and $124{,}000-24{,}000=100{,}000$.

Common mistake avoided: Using $q_2$ or $q_3$ as the unconditional probability of death in that year ignores prior survival. For year 3, for example, the correct probability is $0.99(0.98)(0.03)=0.029106$, not $0.03$.

Common Checks and Exam Traps

The increasing-benefit calculation is simple, but errors often enter through timing or by confusing the total benefit with the insurer’s net exposure. Before finalizing a calculation, check the following:

Use the account value at the claim time. Do not substitute a beginning-of-month or prior-year value if transactions occur before the stated claim time.
Add account value for the benefit. Under the option defined here, the death benefit is $S+A(t)$, not $S$ alone.
Subtract account value for net amount at risk. It is $B(t)-A(t)$, not the full death benefit.
Do not mix transaction orders. Premium allocation, interest crediting, and charges can produce different projected balances if their order changes.
Separate amount from probability. Mortality probabilities determine how likely a claim is, not the conditional benefit amount at a specified claim time.

For this benefit option, a useful final identity is $B(t)-A(t)=S$. It checks the arithmetic after the benefit has been calculated, but it does not replace the need to project the account value correctly.

Check Your Understanding

Use the increasing-benefit formula and the transaction order stated in each problem. Each scenario is hypothetical.

A policy has a specified amount of $125,000 and an account value of $18,750 at death. Find the death benefit and net amount at risk. (Answer: death benefit $143,750; net amount at risk $125,000)
A policy has a $90,000 specified amount and an account value of $10,000 at the start of a month. A $200 allocation is added first, monthly interest of 0.5% is credited next, and a $30 charge is deducted last. Find the month-end death benefit and net amount at risk. (Answer: account value $10,221; death benefit $100,221; net amount at risk $90,000)
A policy has an $80,000 specified amount. Its end-of-year account values are $6,000 and $9,000 in years 1 and 2. Conditional death probabilities are 0.02 and 0.03. Find the expected undiscounted claim payment per policy issued over those two years, with claims paid at the stated year-end amounts. (Answer: $4,336.60)
A candidate reports a $300,000 net amount at risk for a policy with a $300,000 specified amount and a $45,000 account value under the increasing-benefit option. Give the correct death benefit and net amount at risk. (Answer: death benefit $345,000; net amount at risk $300,000)
A policy’s specified amount is $100,000. Its account value rises from $12,000 to $16,000 between two claim dates. By how much does the death benefit change, and what happens to the net amount at risk? (Answer: the death benefit increases by $4,000; the net amount at risk remains $100,000)

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