Death Claim Calculation Workshop

Introduction

A universal life death claim depends on more than the policy’s stated face amount. The account value, the selected death benefit option, any contractual minimum benefit, and the timing of death can all affect the amount payable. The calculation must keep three quantities distinct: the account value, the death benefit paid, and the insurer’s net amount at risk.

This tutorial works through those quantities using hypothetical policy terms. Because contract wording and processing conventions can differ, each example states its assumptions explicitly. In particular, a corridor factor is supplied as part of the hypothetical contract; it is not a universal factor that can be assumed for every policy.

Definition: Let $S$ be the specified amount, $AV$ the account value immediately before the claim is processed, and $c$ the contract’s corridor factor for the claim date. Under the conventions used here, Option A (level) pays $DB_A=\max(S,cAV)$, while Option B (increasing) pays $DB_B=\max(S+AV,cAV)$. The net amount at risk is $NAR=DB-AV$. The death benefit $DB$ is the gross amount payable to the beneficiary; the NAR is a measure of the portion not represented by the account value.

Set the Claim-Date Values Before Choosing the Benefit

The account value used in the claim formula is the value at the time of death under the policy’s stated timing convention. It is not automatically the value at the start of the policy year, the end of a full year, or the surrender value. A premium, premium load, interest credit, monthly deduction, or partial withdrawal may have occurred before death and must be reflected if the contract says it has occurred by the claim date.

For a worked projection, this tutorial will sometimes stipulate a simplified quarterly account process. At the start of each quarter, the account value is known. Interest is credited to that value, then a quarterly administrative charge and a cost-of-insurance charge are deducted at quarter-end. In those examples, the cost-of-insurance charge is calculated from the specified amount less the account value at the start of the quarter, subject to a floor of zero. This is an explicit exercise convention, not a claim that all universal life contracts use this exact schedule.

Calculation order: First project the account value through the claim date using the contract’s transaction timing. Then calculate the benefit under the selected option, including any corridor floor. Finally subtract the claim-date account value from the death benefit to obtain NAR. Do not treat NAR as an additional payment to the beneficiary.

Worked Claims Under the Two Options

The formulas show why identifying the option matters. If the corridor does not bind, Option A’s benefit is the specified amount, whereas Option B’s benefit includes the account value in addition to the specified amount. The same account value therefore produces different death benefits and different NARs.

Worked Example: Projecting a Policy-Year Account and Calculating Both Options

A hypothetical policy has an opening account value of $10,000. A $2,000 premium is paid at the start of the year, with a 5% premium load deducted immediately. The account then earns 3% per quarter. At each quarter-end, the contract deducts a $15 administrative charge and a cost-of-insurance charge equal to $2 per $1,000 of the specified amount less the account value at the start of that quarter. The specified amount is $50,000. Death occurs at the end of the fourth quarter, after that quarter’s charges. The corridor factor is 2.5. Calculate the claim under both options.

Method and premium processing. The load is $0.05(2{,}000)=\$100$, so the net premium added to the account is $2{,}000-100=\$1{,}900$. The account immediately after the premium is $10{,}000+1{,}900=\$11{,}900$.

For each quarter, the cost-of-insurance rate is $2/1{,}000=0.002$ times the beginning-of-quarter NAR basis. The specified account-credit and charge order is applied as follows.

Quarter 1. Interest is $0.03(11{,}900)=\$357.00$. The beginning-of-quarter NAR basis is $50{,}000-11{,}900=\$38{,}100$, so the insurance charge is $0.002(38{,}100)=\$76.20$. Thus the quarter-end account value is $11{,}900+357.00-76.20-15=\$12{,}165.80$.

Quarter 2. Interest is $0.03(12{,}165.80)=\$364.974$. The NAR basis is $50{,}000-12{,}165.80=\$37{,}834.20$, giving an insurance charge of $0.002(37{,}834.20)=\$75.6684$. The account value is $12{,}165.80+364.974-75.6684-15=\$12{,}440.1056$.

Quarter 3. Interest is $0.03(12{,}440.1056)=\$373.203168$. The NAR basis is $50{,}000-12{,}440.1056=\$37{,}559.8944$, and the insurance charge is $0.002(37{,}559.8944)=\$75.1197888$. The account value is $12{,}440.1056+373.203168-75.1197888-15=\$12{,}723.1889792$.

Quarter 4. Interest is $0.03(12{,}723.1889792)=\$381.695669376$. The NAR basis is $50{,}000-12{,}723.1889792=\$37{,}276.8110208$, and the insurance charge is $0.002(37{,}276.8110208)=\$74.5536220416$. The account value at death is $12{,}723.1889792+381.695669376-74.5536220416-15=\$13{,}015.3310265344$, or $13,015.33 to the nearest cent.

Option A. The corridor amount is $2.5(13{,}015.3310265344)=\$32{,}538.327566336$. Since this is below the $50,000 specified amount, the benefit is $50,000. The NAR is $50{,}000-13{,}015.3310265344=\$36{,}984.6689734656$, or $36,984.67.

Option B. The amount before the corridor test is $50{,}000+13{,}015.3310265344=\$63{,}015.3310265344$, which exceeds the corridor amount. The benefit is therefore $63,015.33, and the NAR is $63{,}015.3310265344-13{,}015.3310265344=\$50{,}000.00$.

Check and common mistake. Under Option B, the benefit already includes the account value. Adding the $13,015.33 account a second time would incorrectly report a claim of $76,030.66. The correct Option B payment is $63,015.33; the NAR is not a second beneficiary payment.

When the Corridor Floor Determines the Claim

A corridor floor matters when $cAV$ exceeds the benefit otherwise payable under the selected option. The comparison must be made separately for each option. A corridor can bind under Option A but not Option B, or it can bind under both, depending on $S$, $AV$, and $c$.

Worked Example: A Binding Corridor Under Option A

At the claim date, a hypothetical policy has a $72,000 specified amount and an account value of $36,000. The contract’s corridor factor is 2.25. Calculate the benefit and NAR under each option.

Method. First calculate the corridor amount: $2.25(36{,}000)=\$81{,}000$.

Under Option A, the amount before applying the corridor is $72,000. Since $81{,}000>72{,}000$, the payable benefit is $DB_A=\max(72{,}000,81{,}000)=\$81{,}000$. The NAR is $81{,}000-36{,}000=\$45{,}000$.

Under Option B, the amount before applying the corridor is $72{,}000+36{,}000=\$108{,}000$. This already exceeds the $81,000 floor, so $DB_B=\$108{,}000$. The NAR is $108{,}000-36{,}000=\$72{,}000$.

Check and common mistake. The corridor does not replace the specified amount with a percentage of the specified amount. It is a floor calculated here from the account value, as defined by the hypothetical contract. Applying it to $72,000 instead would give an unsupported figure and the wrong claim.

Death Before the End of a Projection Period

A full policy-year projection cannot be used when death occurs partway through that year unless the contract specifically says to use that value. The account should be projected only through the transactions that have occurred by the claim date. The following example uses two completed quarters of a stipulated four-quarter process.

Worked Example: Calculating a Midyear Claim

A hypothetical policy begins the year with an account value of $18,000. A $4,000 premium is paid at the start of the year and is subject to a 5% load. The account earns 2.5% each quarter. At the end of each completed quarter, a $12 administrative charge and a cost-of-insurance charge of $1 per $1,000 of the $60,000 specified amount less the beginning-of-quarter account value are deducted. Death occurs immediately after the second quarter’s charges. The corridor factor is 2.4. Calculate the claim under both options.

Method and premium processing. The load is $0.05(4{,}000)=\$200$, leaving a net premium of $3,800. The account at the start of the first quarter is $18{,}000+3{,}800=\$21{,}800$.

Quarter 1. Interest is $0.025(21{,}800)=\$545$. The insurance charge is $(60{,}000-21{,}800)/1{,}000=\$38.20$. After the $12 administrative charge, the account is $21{,}800+545-38.20-12=\$22{,}294.80$.

Quarter 2. Interest is $0.025(22{,}294.80)=\$557.37$. The insurance charge is $(60{,}000-22{,}294.80)/1{,}000=\$37.7052$. The account immediately before the claim is $22{,}294.80+557.37-37.7052-12=\$22{,}802.4648$, or $22,802.46 to the nearest cent.

The corridor amount is $2.4(22{,}802.4648)=\$54{,}725.91552$, or $54,725.92 to the nearest cent. It is below the $60,000 specified amount. Option A therefore pays $60,000, with NAR $60{,}000-22{,}802.4648=\$37{,}197.5352$, or $37,197.54. Option B pays $60{,}000+22{,}802.4648=\$82{,}802.4648$, or $82,802.46, with NAR of $60,000.00.

Check and common mistake. The account at the end of a hypothetical fourth quarter is not relevant because death occurred after quarter two. Projecting two more quarters would include credits and deductions after the claim date and would overstate the account value used in this calculation.

Why Net Amount at Risk Is Death Benefit Less Account Value

The NAR calculation is an accounting decomposition of the claim, not a second benefit formula. In the simplified interpretation used here, the account value is the portion of the claim represented by funds already accumulated in the policy. The amount in excess of that account value is the insurer’s net exposure for the death benefit.

$$ DB=AV+(DB-AV) $$

The first term on the right is the account value; the second is the NAR. Thus, defining $NAR=DB-AV$ makes the two parts add back to the total death benefit. For Option A, if the corridor does not bind, this gives $NAR=S-AV$. For Option B, if the corridor does not bind, it gives $NAR=(S+AV)-AV=S$. If the corridor binds under either option, then $DB=cAV$, so $NAR=(c-1)AV$.

These identities are useful checks, but they depend on the benefit definitions stated here. If a contract defines a different benefit, includes a rider payment, or specifies a different account-value treatment at death, use the actual contract terms. NAR is not necessarily the amount of cash the insurer pays in addition to the stated death benefit.

Common Claim-Calculation Errors

Adding the account value twice. Under the increasing option, the account value is already included in $S+AV$. Do not add it again after calculating the death benefit.
Confusing benefit with NAR. The beneficiary’s gross payment is $DB$, not $NAR$. NAR is calculated by subtracting the account value from that benefit.
Ignoring a binding corridor. Compare the corridor amount with the benefit under the selected option. Do not assume the specified amount always determines the claim.
Using the wrong date’s account value. Reflect premiums, credits, and deductions only as required through the death date. A full-year value is not automatically appropriate for a midyear death.
Changing the charge basis silently. A cost-of-insurance charge may be defined using a contract-specific basis and timing. Use the basis provided rather than substituting a different NAR definition.

Key takeaway: Project the account to the claim date, apply the selected benefit option and its corridor floor, then calculate $NAR=DB-AV$. Keep the gross claim, the account value, and the NAR separate throughout the work.

Check Your Understanding

For each hypothetical policy, apply the stated benefit convention and round money to the nearest cent where needed.

At death, $AV=\$24{,}000$, $S=\$60{,}000$, and $c=2.5$. Under Option A, find the death benefit and NAR. (Answer: death benefit $60,000.00; NAR $36,000.00)
At death, $AV=\$12{,}500$, $S=\$45{,}000$, and $c=2.0$. Under Option B, find the corridor amount, death benefit, and NAR. (Answer: corridor $25,000.00; death benefit $57,500.00; NAR $45,000.00)
At death, $AV=\$30{,}000$, $S=\$50{,}000$, and $c=1.8$. Under Option A, determine whether the corridor binds, then find the death benefit and NAR. (Answer: corridor binds; death benefit $54,000.00; NAR $24,000.00)
A policy has $AV=\$28{,}400$, $S=\$80{,}000$, and $c=2.1$. Calculate the Option A and Option B death benefits and NARs. (Answer: Option A benefit $80,000.00 and NAR $51,600.00; Option B benefit $108,400.00 and NAR $80,000.00)
An Option B policy has $AV=\$29{,}000$, $S=\$63{,}000$, and $c=2.4$. A trainee adds the account value to the death benefit a second time. Find the correct benefit and NAR, and state the trainee’s incorrect total. (Answer: correct benefit $92,000.00; NAR $63,000.00; incorrect double-counted total $121,000.00)

What You'll Learn