Bonus Calculations For Endowment And Whole-Life Claims

Why Claim Type and Timing Matter

A declared reversionary bonus can increase a policy benefit, but the amount payable depends on the contract: the bonus basis, the number of declarations already made, and the event that triggers the claim. An endowment policy may pay at maturity if the insured survives to the specified date, while a whole-life policy pays on death whenever it occurs. The same bonus scale can therefore produce different claim amounts at different times.

This tutorial calculates contractual benefits, not expected values or present values. For each example, the interest rate, mortality assumption, and probability distribution are therefore stated as not applicable: the calculation is conditional on a specified claim event and uses no survival probabilities. No interest discounting is applied to a benefit payable at the claim date.

Definition: A vested reversionary bonus is a bonus declared under the policy terms that has become part of the guaranteed benefit. A claim calculation includes the vested additions applicable at the claim date, along with the basic sum assured and any other bonus explicitly payable under the contract. A terminal bonus, if the contract provides one, is a separate addition and must not be assumed to exist or be included without an applicable term.

Set Out the Contract Before Calculating

Before doing arithmetic, translate the policy wording into a benefit rule. Record the basic sum assured, whether the bonus is simple or compound, its rate and base, when declarations occur, and the claim event and date. Also check whether an interim or terminal bonus is specified. These details determine both the bonus amount and which declarations count.

For a simple reversionary bonus at rate $b$ per year on the original sum assured $S$, if $n$ bonuses have been declared and vested, the accumulated bonus is $n b S$. The corresponding benefit, when the contract pays the basic sum assured plus these additions, is $S(1+nb)$.

For a compound reversionary bonus at rate $b$ per declaration on the current guaranteed amount, let $G_k$ be the guaranteed amount after the $k$-th declaration. The recurrence is $G_k=G_{k-1}(1+b)$, with $G_0=S$. After $n$ declarations, $G_n=S(1+b)^n$. This formula applies only when the stated compound bonus is added to the prior guaranteed amount at each declaration. A bonus calculated on the original sum assured instead follows a different rule.

The timing convention matters. A claim occurring after the fifth declaration includes five declared bonuses, not a sixth bonus merely because the sixth policy anniversary is near. If the claim date falls between declarations, use only the declarations already made unless the contract separately specifies an interim bonus.

Worked Example: Endowment Maturity With Simple Bonuses

A hypothetical 10-year endowment has a basic sum assured of $100,000. At the end of each policy year, a simple reversionary bonus of $25 per $1,000 of basic sum assured is declared. The insured survives to maturity, immediately after the tenth declaration. No terminal bonus or other addition is payable. State the maturity benefit.

Assumptions. The claim is a survival claim at the stated maturity date. Interest rate: not applicable to the contractual amount. Mortality assumption: survival to maturity is given; no mortality model is used. Probability distribution: none is needed. The bonus rate and base are those stated in the contract.

Method. Convert the sum assured into $1,000 units:

\frac{100{,}000}{1{,}000}=100

Each annual declaration therefore adds $100\times \$25=\$2,500$. There are ten completed declarations, so the total vested bonus is:

10\times \$2{,}500=\$25{,}000

The maturity benefit is the basic sum assured plus the vested additions:

\$100{,}000+\$25{,}000=\boxed{\$125{,}000}

Check. The simple bonus is 2.5% of the original sum assured each year, so ten declarations add 25% of $100,000, or $25,000. The result agrees. The common mistake avoided here is treating the simple bonus as compound and applying later rates to accumulated bonuses.

Why the Compound-Bonus Formula Works

The compound formula follows directly from the contract recurrence. At each declaration, the newly guaranteed amount is the previous guaranteed amount plus a fraction $b$ of it. Thus:

G_k=G_{k-1}+bG_{k-1}=(1+b)G_{k-1}

Starting from $G_0=S$, the first declaration gives $G_1=S(1+b)$. Applying the same rule again gives $G_2=S(1+b)^2$. Repeating the recurrence $n$ times yields:

$$ G_n=S(1+b)^n $$

This derivation also explains why the result should not be used for a simple bonus on the original sum assured: in that contract, each addition is $bS$, not $bG_{k-1}$. The bonus basis, rather than the word “bonus” alone, decides the calculation.

Worked Example: Whole-Life Death Benefit After Five Declarations

A hypothetical whole-life policy has a basic sum assured of $80,000. A compound reversionary bonus of 3% is declared at each policy anniversary and added to the guaranteed amount. The insured dies immediately after the fifth declaration. The policy specifies no terminal or interim bonus. Calculate the death benefit.

Assumptions. The claim is a death claim immediately after declaration five. Interest rate: not applicable to the claim amount. Mortality assumption: death at the stated time is given; no mortality model is used. Probability distribution: none is needed. The 3% rate applies to the guaranteed amount immediately before each declaration.

Method. Five declarations have been made, so use $n=5$ in the compound accumulation:

G_5=\$80{,}000(1.03)^5

To show the accumulation step by step:

\begin{aligned} G_1&=\$80{,}000(1.03)=\$82{,}400\\ G_2&=\$82{,}400(1.03)=\$84{,}872\\ G_3&=\$84{,}872(1.03)=\$87{,}418.16\\ G_4&=\$87{,}418.16(1.03)=\$90{,}040.7048\\ G_5&=\$90{,}040.7048(1.03)=\$92{,}741.925944 \end{aligned}

Rounded to the nearest cent, the death benefit is $92,741.93. The vested bonus portion is $92,741.93 minus $80,000, or $12,741.93, with the final benefit rounded only after accumulation.

Check. The accumulated amount is greater than the basic sum assured, as a positive compound bonus requires. The common mistake avoided is counting a sixth bonus because death occurred after the fifth anniversary; the contract specifies one declaration at each anniversary, and only five have occurred.

Comparing an Endowment Claim With a Whole-Life Claim

The calculation structure may be identical while the claim trigger differs. Under an endowment contract, a maturity benefit is payable only if the insured survives to the stated maturity date; a death benefit during the term is governed by the death-benefit terms instead. Under a whole-life contract, the death benefit is payable on death, with the applicable vested bonuses determined by the declarations made by then. Do not substitute a maturity date for a death date or assume that a whole-life policy has an endowment maturity benefit.

The following comparison uses the same basic sum assured and compound rate, but different claim times. It isolates the effect of the declaration count; it does not imply that the two hypothetical policies otherwise have identical contract terms.

Worked Example: Same Bonus Scale, Different Claim Dates

A hypothetical endowment and a hypothetical whole-life policy each have a $60,000 basic sum assured. Both declare a 2% compound reversionary bonus on the current guaranteed amount at each policy anniversary. The endowment matures immediately after its twelfth declaration, and the insured survives to that date. The whole-life insured dies 7.5 years after the policy starts, after the seventh declaration but before the eighth. Neither policy provides an interim or terminal bonus. Calculate each benefit and compare them.

Assumptions. Interest rate: not applicable to benefits at the claim dates. Mortality assumption: endowment survival to year 12 and whole-life death at year 7.5 are specified events; no mortality model is used. Probability distribution: none is needed. Declaration timing is annual, and the whole-life claim occurs before declaration eight.

Endowment maturity benefit. Twelve declarations have vested:

\begin{aligned} G_{12}&=\$60{,}000(1.02)^{12}\\ (1.02)^{12}&=1.26824179456\\ G_{12}&=\$76{,}094.5076736\\ \text{Maturity benefit}&=\boxed{\$76{,}094.51} \end{aligned}

Whole-life death benefit. The death occurs after seven declarations, so the eighth bonus is not included:

\begin{aligned} G_7&=\$60{,}000(1.02)^7\\ (1.02)^7&=1.14868566744\\ G_7&=\$68{,}921.1400464\\ \text{Death benefit}&=\boxed{\$68{,}921.14} \end{aligned}

The maturity benefit is $7,173.37 greater, reflecting five additional declarations: $76,094.51 minus $68,921.14. Check. Since $G_{12}=G_7(1.02)^5$, the later amount must exceed the earlier one. The common mistake avoided is assigning eight declarations to the death claim just because the policy has entered its eighth policy year.

A Reliable Claim-Calculation Sequence

A short, consistent sequence reduces errors when policy wording mixes a benefit event with a bonus rule.

Identify the claim event.
Determine whether the claim is for death, survival to endowment maturity, or another stated event. Apply only the benefit rule for that event.

Count completed declarations.
Use the declaration dates and claim date, not merely the policy year number. Exclude any declaration that has not occurred unless an explicit interim-bonus term applies.

Apply the stated bonus base.
For a simple bonus on the original sum assured, add the same amount at each declaration. For a compound bonus on the current guaranteed amount, multiply by $1+b$ at each declaration.

Assemble the payable benefit.
Add the basic amount and applicable vested additions. Include a terminal bonus only if the terms make it payable for this claim event and duration.

Check the result.
Confirm the amount is consistent with the number of bonuses, their basis, and the claim trigger. Round the final monetary result as required.

Common Exam Traps

Using the wrong bonus base. A rate on the original sum assured gives a different result from a rate on the existing guaranteed amount. Read the base before choosing the formula.
Counting a future declaration. A claim between anniversaries does not automatically include the next annual bonus. Check whether an interim bonus is explicitly provided.
Confusing maturity and death claims. An endowment maturity benefit requires survival to maturity. A death during the term must be calculated under the death-benefit provision, not relabelled as maturity.
Adding an unspecified terminal bonus. A terminal bonus is not implied by the presence of vested reversionary bonuses. Include it only when its terms and eligibility are given.
Discounting a claim amount unnecessarily. A contractual amount payable at the claim date is not a present value. Apply discounting only when the question asks for a value at another date.

Key takeaway: A claim benefit is determined by the claim event, the declarations actually made, and the bonus base stated in the contract. Endowment maturity and whole-life death calculations can use the same bonus mechanics, but their triggering events and claim dates need not be the same.

Check Your Understanding

For each problem, use the stated contract terms and claim timing. No present-value calculation is required.

A hypothetical 8-year endowment has a basic sum assured of $75,000 and a simple annual bonus of $18 per $1,000 of basic sum assured. The insured survives to maturity immediately after declaration eight. No other bonus is payable. Find the maturity benefit. (Answer: $85,800.00)
A hypothetical whole-life policy has a basic sum assured of $50,000 and a compound bonus of 2.5% on the current guaranteed amount at each anniversary. Death occurs immediately after declaration four. No terminal bonus is payable. Find the death benefit. (Answer: $55,190.64)
A hypothetical 15-year endowment has a basic sum assured of $120,000 and a compound annual bonus of 1.5% on the current guaranteed amount. The insured survives to maturity immediately after declaration 15. Find the maturity benefit to the nearest cent. (Answer: $150,027.85)
A hypothetical whole-life policy has a basic sum assured of $90,000 and a compound bonus rate of 3% per anniversary on the current guaranteed amount. Death occurs 6.4 years after issue, after declaration six but before declaration seven. No interim or terminal bonus applies. Find the death benefit to the nearest cent. (Answer: $107,464.71)
A hypothetical 20-year endowment has a basic sum assured of $40,000 and a simple bonus of $30 per $1,000 of basic sum assured at each anniversary. The maturity claim is payable immediately before the declaration scheduled on the 20th anniversary. The insured survives to that date, and no other bonus applies. How many bonuses count, and what is the benefit? (Answer: 19 bonuses; $62,800.00)

What You'll Learn