Introduction
A terminal bonus calculation has two separate choices: which rate applies and which amount the rate is applied to. A table may vary its rate by policy duration, while the benefit base may be the original sum assured, accumulated vested bonuses, or the total guaranteed benefit. Choosing the correct rate but the wrong base can materially change the claim amount.
This tutorial treats each stated rate as the rate to use for the hypothetical calculation. It focuses on reading a duration-based scale and applying its specified base. It does not determine whether a particular claim event qualifies for a terminal bonus.
Reading a Duration-Based Scale
A duration table assigns a rate to one or more ranges of policy duration. For example, a hypothetical scale might show one rate for durations 1–9, a higher rate for durations 10–14, and another rate for durations 15 and above. First determine the duration measure and the relevant band. Unless the problem specifies a different convention, use the stated policy duration at the calculation date and apply the band that includes it. A duration at a boundary belongs to only one band; read the table's endpoints rather than rounding the duration into a preferred band.
The rate table alone does not tell you the amount on which the percentage is calculated. That information is supplied separately by the wording or a base column. In the examples below, “18% of sum assured” means 18% of the original sum assured, not the sum assured plus later additions.
| Specified base | Meaning of base | Terminal bonus |
|---|---|---|
| Original sum assured | The sum assured at issue, excluding later vested additions | Rate × original sum assured |
| Vested bonuses | The accumulated additions already vested under the policy | Rate × vested bonuses |
| Total guaranteed benefit | The sum assured plus vested bonuses in this tutorial's examples | Rate × (sum assured + vested bonuses) |
These are different bases, not alternative ways to describe the same amount. If the vested bonuses are positive, the total guaranteed benefit exceeds the original sum assured. A rate applied to total guaranteed benefit therefore produces a larger terminal bonus than the same rate applied only to the original sum assured. The contractual definition of the base controls; do not infer it from the policy's benefit components.
A Reliable Calculation Method
Use the policy duration at the stated calculation date and identify the table band containing it.
Record both items. Do not carry a rate from one duration band or a base from another row.
For a total guaranteed benefit base, add the components included by the definition before multiplying.
Multiply the decimal form of the rate by the specified base, then add the bonus to the benefit components that are payable.
Confirm that the bonus uses the stated base, that the amount has the same currency units as the base, and that vested bonuses have been included once in the total.
Why the Calculation Is a Product
A rate stated as a percentage of a benefit base expresses the terminal bonus as that fraction of the base. If the rate is 18%, each dollar of the named base contributes 18 cents to the bonus. For a base of \(B\) dollars, the contributions from all \(B\) dollars sum to \(0.18B\). More generally, for rate \(r\), the amount is \(rB\), with the rate written as a decimal in the multiplication.
Here \(G\) is the guaranteed benefit payable before adding this terminal bonus. If the base itself is defined as the total guaranteed benefit, then \(B=G\) for this calculation. This does not mean the terminal bonus is already included in \(G\): the scale defines the base before the terminal bonus is added. The distinction prevents circular calculations and double counting.
Worked Example: Rate Applied to the Original Sum Assured
A hypothetical participating policy has an original sum assured of $125,000 and $31,250 of vested bonuses at the calculation date. Its terminal bonus scale is 10% for durations 1–9, 18% for durations 10–14, and 24% for duration 15 and above. The scale specifies that the rate is applied to the original sum assured. Calculate the terminal bonus and total benefit at duration 12.
Method. Select the duration-12 rate, use the original sum assured as the base, then add the terminal bonus to the guaranteed components.
Duration 12 is in the 10–14 band, so \(r=18\%=0.18\). The specified base is the original sum assured, \(B=\$125{,}000\); the vested bonuses are not part of this base.
The guaranteed benefit before the terminal bonus is \(\$125{,}000+\$31{,}250=\$156{,}250\). Therefore the total benefit is \(\$156{,}250+\$22{,}500=\$178{,}750\).
Check. The bonus is 18% of $125,000, not 18% of $156,250. The total includes the vested bonuses once and the terminal bonus once.
Common mistake avoided. Applying 18% to the total guaranteed benefit would give $28,125 and overstate the terminal bonus by $5,625. That calculation uses a different base from the one specified.
Worked Example: Rate Applied to Vested Bonuses
A hypothetical policy has an original sum assured of $92,000 and vested bonuses of $18,400. Its scale gives a terminal bonus rate of 30% for duration 8 and states that the rate applies to vested bonuses only. Calculate the terminal bonus and the total benefit.
Method. Identify the stated duration-8 rate and use the vested bonus amount, rather than the sum assured or the combined guaranteed benefit, as the base.
The rate is \(r=30\%=0.30\), and the base is \(B=\$18{,}400\). Thus:
The guaranteed benefit before the terminal bonus is \(\$92{,}000+\$18{,}400=\$110{,}400\). Adding the terminal bonus gives a total benefit of \(\$110{,}400+\$5{,}520=\$115{,}920\).
Check. The terminal bonus is less than the vested bonuses because the rate is less than 100%. The final total exceeds the guaranteed benefit by exactly $5,520.
Common mistake avoided. Multiplying 30% by $92,000 would produce $27,600. That is not a rounding error; it is the result of applying the rate to the wrong benefit base.
Worked Example: Rate Applied to the Total Guaranteed Benefit
A hypothetical contract has a sum assured of $150,000 and vested bonuses of $45,000. At duration 16, the terminal bonus scale specifies a rate of 8% of the total guaranteed benefit, defined here as the sum assured plus vested bonuses. Calculate the terminal bonus and total benefit.
Method. First form the total guaranteed benefit because it is the specified base. Then apply the duration-16 rate and add the terminal bonus.
The total guaranteed benefit, and hence the base, is:
The rate is \(r=8\%=0.08\). Therefore:
The total benefit after the terminal bonus is \(\$195{,}000+\$15{,}600=\$210{,}600\).
Check. The bonus is 8% of the $195,000 guaranteed base, and the total is 108% of that base: \(1.08(\$195{,}000)=\$210{,}600\).
Common mistake avoided. Applying 8% only to the $150,000 sum assured would give $12,000, omitting the vested bonuses from the base. Conversely, adding the terminal bonus into the base before calculating would be circular and is not the stated definition.
Duration Bands and Base Selection Must Be Checked Separately
A useful way to avoid mixing up the two decisions is to make a small calculation record before doing arithmetic:
| Question | What to write down |
|---|---|
| What is the policy duration? | The duration at the calculation date |
| Which rate band contains it? | The exact band and the rate from that band |
| What is the base? | Original sum assured, vested bonuses, or the defined total guaranteed benefit |
| What is the amount payable? | Guaranteed benefit plus the calculated terminal bonus |
Duration and base can interact in a table that has different rates or bases in different rows. For example, one row might specify a percentage of vested bonuses for shorter durations while a later row specifies a percentage of total guaranteed benefit. In that case, select the applicable row first and use both its rate and its base. Do not carry a base from one row into another just because that base was used for a different duration.
At a duration-band boundary, a small change in duration may change the rate abruptly. If a policy moves from duration 9 to duration 10 and the scale increases from 12% to 17%, the rate changes by 5 percentage points; it does not increase by 5% of the old rate. Calculate the benefit under the applicable band rather than interpolating unless the scale explicitly requires interpolation.
Common Errors and Checks
- Using the wrong duration. The rate is selected from the duration at the stated calculation date, not automatically from the number of premiums paid or the policy's issue year label.
- Assuming every rate uses the sum assured. Read the base wording; a percentage of vested bonuses can be much smaller than the same rate applied to the sum assured.
- Including additions in the base when the scale excludes them. If the base is the original sum assured, later vested additions do not enlarge it.
- Omitting vested bonuses from the total benefit. They may be excluded from a particular terminal-bonus base but still form part of the guaranteed benefit payable.
- Counting vested bonuses twice. Add them once when forming the guaranteed benefit. If the total guaranteed benefit is the base, do not add the same vested bonuses a second time after forming that base.
- Applying a percentage as a whole number. Use \(18\%=0.18\), not 18, in a multiplication.
A final reasonableness check is to compare the terminal bonus with its base. At a rate below 100%, the bonus must be less than the specified base. Also verify that the total benefit equals the guaranteed benefit before the bonus plus the terminal bonus, and not merely the terminal bonus itself.
Check Your Understanding
For each problem, identify the duration band and specified base before calculating. Amounts are hypothetical.
- A policy has a $70,000 original sum assured and $14,000 in vested bonuses. At duration 11, the rate is 16% of the original sum assured. Find the terminal bonus and total benefit. (Answer: terminal bonus $11,200; total benefit $95,200.)
- A policy has a $110,000 sum assured and $27,500 of vested bonuses. At duration 14, the rate is 22% of vested bonuses. Find the terminal bonus and total benefit. (Answer: terminal bonus $6,050; total benefit $143,550.)
- A policy has a $160,000 sum assured and $40,000 of vested bonuses. At duration 19, the rate is 9.5% of the total guaranteed benefit, defined as the sum assured plus vested bonuses. Find the terminal bonus and total benefit. (Answer: terminal bonus $19,000; total benefit $219,000.)
- A scale applies 12% of the original sum assured at durations 1–9 and 17% of the original sum assured at durations 10 and above. A policy has an $84,000 sum assured and $22,000 of vested bonuses. Find the total benefit at duration 9 and at duration 10, and the increase between the two totals. (Answer: duration 9 total $116,080; duration 10 total $120,280; increase $4,200.)
- A scale applies 20% of vested bonuses at durations 1–9 and 7% of total guaranteed benefit at durations 10 and above. A policy has a $125,000 sum assured and $35,000 in vested bonuses. At duration 12, calculate the terminal bonus and total benefit. (Answer: terminal bonus $11,200; total benefit $171,200.)