Introduction
A participating policy can provide several different kinds of value: a guaranteed benefit, reversionary bonus additions declared during the policy term, cash dividends paid along the way, and a terminal bonus payable only when a claim arises. Calculating the final death or maturity amount requires more than adding every amount mentioned in the policy history. The key questions are what remains payable at the claim date and which amounts form the base for each bonus.
This tutorial calculates claim amounts for hypothetical policies with mixed bonus types. It distinguishes the amount payable at death or maturity from cash dividends already received. It does not discount benefits to a valuation date: the calculations are nominal amounts at the claim date, not present values.
Set the Claim-Date Components Before Calculating
Write the claim as a sum of amounts payable at the claim date. Let \(G\) be the guaranteed benefit for the relevant claim event, and let \(R\) be the total vested reversionary additions included in that benefit. If the terminal bonus is a proportion \(b\) of \(G+R\), then the claim amount is
This expression is valid only when the contract defines the terminal-bonus base as the guaranteed benefit plus vested additions. A policy may instead specify a different base, a fixed terminal-bonus amount, or different terms for death and maturity. The contract definition controls.
Cash dividends paid before the claim do not appear in this formula. If the question asks for the policyholder’s total cash received over the policy’s life, add those past dividends separately to the claim amount. Do not add them to the claim itself or to a terminal-bonus base unless the contract explicitly says they are included.
Decide whether the calculation is for death or maturity, and identify how many bonus declarations have occurred before that event.
Apply each declared simple or compound bonus according to its stated base. Include only additions that have vested by the claim date.
Use the specified percentage or amount and the precise contractual base for this claim event.
Report the claim amount on its own. Add prior dividends only if the requested measure is total cash received.
Why the Components Are Added This Way
The claim amount is a payment at a particular event date. The guaranteed benefit and vested reversionary additions are payable at that date under the assumed contract terms. A terminal bonus is also payable then, but it is calculated from its own specified base. Thus, when that base is \(G+R\), the policy pays \(G+R\) plus a further \(b(G+R)\).
A cash dividend already paid is a separate earlier cash flow. Adding it again to \(C\) would count the same payment twice if the question is asking for the claim-date payment. Conversely, leaving it out of a calculation of all cash received would omit a payment. This distinction follows from the timing and definition of the requested quantity, not from whether the dividend is described as a policy benefit.
For simple additions, each declaration is calculated on the original specified base; for compound additions, later declarations may include earlier additions. The description “reversionary bonus” by itself does not determine which method applies. Use the stated declaration basis, then apply any terminal bonus only after the vested additions have been totalled.
Worked Example: Maturity With Simple Additions and Paid Dividends
A hypothetical three-year endowment has a guaranteed maturity benefit of $20,000. At each of the three anniversaries, a declared simple reversionary addition of $300 becomes vested. A $180 cash dividend is paid at each anniversary. At maturity, a terminal bonus of 5% is payable on the guaranteed benefit plus vested additions. Find (a) the maturity claim and (b) total cash received over the policy term, including the dividends.
Assumptions. The effective annual interest rate is \(i=0.04\), but no discounting is required because the requested amounts are at the payment dates. For a separate mortality description, assume discrete annual deaths with \(q_{50}=0.010\), \(q_{51}=0.012\), and \(q_{52}=0.014\), conditional on being in force at the start of each year. The calculation is conditional on survival to maturity; these mortality probabilities do not change the specified claim amount. Dividends and bonuses are as stated, with no interest credited to paid dividends.
Method. First total the vested simple additions. Each declaration is $300, so
The terminal-bonus base is the guaranteed benefit plus those additions:
The terminal bonus is \(0.05(20{,}900)=1{,}045\). Therefore the maturity claim is
Three dividends of $180 have already been paid, for a total of \(3(180)=\$540\). Total cash received over the term, counting those payments as well as the maturity claim, is \(\$21{,}945+\$540=\$22{,}485\).
Check. The claim consists of the $20,000 guarantee, $900 in vested additions, and $1,045 terminal bonus. The $540 of dividends appears only in the lifetime cash total. The common mistake avoided is adding the past dividends to the terminal-bonus base or counting them as part of the maturity payment.
Worked Example: Death Claim With Compound Additions
A hypothetical participating policy has a guaranteed death benefit of $40,000. Two annual compound reversionary bonuses have been declared: each is 1.5% of the guaranteed benefit plus all previous vested additions. Cash dividends of $250 were paid at each of those anniversaries. The insured dies during the following policy year, before another bonus is declared. A terminal bonus of 3% is payable on the guaranteed death benefit plus vested additions. Calculate the death claim and the total cash received from the stated bonuses, dividends, and claim.
Assumptions. The effective annual interest rate is \(i=0.03\); no discounting is applied to amounts at their payment dates. Assume discrete annual mortality with \(q_{60}=0.008\), \(q_{61}=0.009\), and \(q_{62}=0.010\), conditional on being in force at the start of each year. The death is during the third year, after two declarations; the stated mortality probabilities identify the model but do not alter the conditional claim calculation. The dividends have been paid in cash, with no accumulation.
Method. At the first anniversary, the addition is
At the second anniversary, the compound-bonus base includes the first addition:
The total vested additions are \(R=600+609=1{,}209\). The terminal-bonus base is \(40{,}000+1{,}209=41{,}209\), so the terminal bonus is \(0.03(41{,}209)=1{,}236.27\). Thus,
The two paid dividends total \(2(250)=\$500\). The total cash received from the stated components is therefore \(\$42{,}445.27+\$500=\$42{,}945.27\).
Check. The second bonus is larger than the first because its stated base includes the first addition. The terminal bonus is calculated after both additions are included. The common mistake avoided is applying the second declaration to $40,000 alone, which would incorrectly make both additions $600.
Worked Example: Comparing Death and Maturity Values
A hypothetical four-year policy has a guaranteed benefit of $30,000 on either death or maturity. A simple addition of $240 is declared at each completed anniversary. Cash dividends of $125 are paid at those anniversaries. The terminal bonus is 2% of the guaranteed benefit plus vested additions on death, and 4% of that base on maturity. Find (a) the death claim if death occurs during the third policy year after two anniversaries and (b) the maturity claim if the policy remains in force for all four years. Also find the total cash received in each case, including dividends paid before the event.
Assumptions. The effective annual interest rate is \(i=0.025\), with no discounting of claim-date amounts. Assume discrete annual mortality with \(q_{55}=0.006\), \(q_{56}=0.007\), \(q_{57}=0.008\), and \(q_{58}=0.009\), conditional on being in force at the start of each year. The death calculation is conditional on death during year three after exactly two declarations; the maturity calculation is conditional on survival through four years. Dividends are paid in cash and earn no interest.
Death claim. Two declarations have occurred, so vested additions total \(R_D=2(240)=480\). The death terminal-bonus base is \(30{,}000+480=30{,}480\). The terminal bonus is \(0.02(30{,}480)=609.60\), giving
Two dividends have been paid, totalling \(2(125)=\$250\). Total cash received in the death scenario is \(\$31{,}089.60+\$250=\$31{,}339.60\).
Maturity claim. Four declarations have occurred, so \(R_M=4(240)=960\). The maturity terminal-bonus base is \(30{,}000+960=30{,}960\), and the maturity terminal bonus is \(0.04(30{,}960)=1{,}238.40\). Therefore,
Four dividends total \(4(125)=\$500\), so total cash received in the maturity scenario is \(\$32{,}198.40+\$500=\$32{,}698.40\).
Check. The maturity claim exceeds the death claim because it includes two additional simple declarations and has a higher terminal-bonus rate. Dividends are counted in the cash totals but not in either claim. The common mistake avoided is using the four-year additions or maturity bonus rate in the earlier death scenario.
Common Exam Traps
A reliable calculation keeps the event, the bonus base, and the payment timing visible. In particular, do not assume that every bonus is calculated on the same base, or that every amount paid during the policy term remains part of the claim.
Other checks that help prevent errors include:
- Count only declarations made by the claim date; a projected future bonus is not automatically vested.
- For compound bonuses, calculate each declaration using the correct accumulated base before moving to the next declaration.
- Read the terminal-bonus base literally. A bonus on the guarantee plus additions is not necessarily a bonus on dividends or on every amount ever paid.
- State whether the requested result is the claim amount or total cash received. They are different whenever prior dividends have been paid.
- Use the death or maturity terms that apply to the actual event; the two claim amounts and bonus rates need not match.
Check Your Understanding
For each hypothetical policy, calculate the requested claim amount using the stated timing and bonus bases. Amounts are nominal at the payment date; do not discount them.
- A three-year maturity benefit has a guarantee of $12,000, three simple vested additions of $175 each, and a terminal bonus of 3% of the guarantee plus additions. Cash dividends of $90 were paid at each anniversary. Find the maturity claim, not total cash received. (Answer: $12,900.75.)
- A death benefit has a guarantee of $18,000 and two compound additions, each 2% of the guarantee plus previous additions. A terminal bonus of 1.5% applies to the guarantee plus all vested additions. Find the death claim after the second declaration. (Answer: $19,008.11.)
- A policy has a $50,000 guaranteed death benefit, three vested simple additions of $400 each, and a 2.5% terminal bonus on the guarantee plus additions. Dividends of $200 were paid at each of the three anniversaries. Find the death claim only. (Answer: $52,480.00.)
- A maturity guarantee of $10,000 receives two compound additions, each equal to 5% of the guarantee plus previous additions. The terminal bonus is 2% of the guarantee plus vested additions. Find the maturity claim. (Answer: $11,245.50.)
- A four-year policy has a $24,000 maturity guarantee, four simple additions each equal to 1% of the guarantee, and a terminal bonus of 5% of the guarantee plus additions. A $300 cash dividend was paid at each anniversary. Find total cash received by maturity, including dividends. (Answer: $27,408.00.)