Introduction
A terminal bonus at maturity is an additional payment determined when a participating policy reaches its maturity date. A duration-based scale can make the bonus rate depend on how long the policy has been in force. To calculate the payment correctly, it is not enough to find a rate: the calculation must also use the duration convention and the eligible benefit base specified by the hypothetical policy terms.
This tutorial focuses on a maturity claim with an expressly stated duration-based terminal-bonus scale. The examples are hypothetical. They assume that the policy remains in force to maturity and that all declared additions described as vested are included in the maturity benefit. They do not calculate the probability or present value of reaching maturity.
Separate Duration, Rate, and Base
Use the duration at the maturity date, not the date on which a calculation happens to be performed. When the terms specify completed policy years, count only whole years completed by maturity. For example, a policy maturing after 11 years and 8 months has 11 completed years. A policy maturing on its 12th anniversary has completed 12 years. The scale wording controls if it defines duration differently.
After finding the duration, select the rate band containing that duration. A rate stated for a band is ordinarily the single rate applied to the eligible base at that duration; it is not automatically a set of marginal rates to apply to successive policy years. The scale or policy terms must say if a different interpretation is intended.
The eligible base is a separate question. A scale might specify a percentage of vested additions, or a percentage of the basic guaranteed benefit plus vested additions. Those bases give different results. A cash dividend paid earlier is not a vested addition held in the maturity benefit, so it is excluded unless the stated scale expressly includes it.
Why the Calculation Has This Form
A percentage rate represents a proportion of a specified amount. If the scale states that the terminal bonus is \(r\) of eligible base \(E\), then one unit of eligible base produces \(r\) units of bonus. For \(E\) units, the bonus is therefore \(rE\). The rate does not determine what \(E\) is: that comes from the scale wording.
The maturity payment then adds the separate amounts payable at maturity. Under the assumptions above, the basic guarantee contributes \(G\), vested additions contribute \(V\), and the terminal bonus contributes \(r(n)E\). Thus \(M=G+V+r(n)E\). This decomposition prevents two common errors: applying the rate to the wrong base, and counting an amount twice.
Apply the duration convention stated in the scale, such as completed policy years, at the maturity date.
Find the one scale band containing that duration and record its rate.
Include only the amounts named as eligible in the scale.
Multiply rate by eligible base, then add the terminal bonus to the distinct maturity benefits payable.
Worked Maturity Calculations
Worked Example: Bonus Rate on Vested Additions
Hypothetical policy. The basic guaranteed maturity benefit is $80,000. The policy earns a simple vested addition of 1.25% of the basic benefit for each completed policy year. It matures exactly on its 12th anniversary. The terminal-bonus scale pays 8% of vested additions for fewer than 10 completed years, 15% for 10 through 14 completed years, and 22% for 15 or more completed years. There are no other maturity amounts. Calculate the payment. The method is to determine duration, calculate vested additions, apply the rate to the named base, and assemble the payment. It avoids applying the rate to the basic benefit when the scale names additions only.
1. Duration and rate. The policy has completed 12 years at its 12th anniversary. Twelve is in the 10-through-14 band, so \(r(12)=15\%=0.15\).
2. Vested additions. The addition for each completed year is \(0.0125\times \$80{,}000=\$1{,}000\). Over 12 completed years, \(V=12\times \$1{,}000=\$12{,}000\).
3. Eligible base and terminal bonus. The scale specifies vested additions as the base, so \(E=\$12{,}000\), not $80,000 or $92,000. Therefore \(T=0.15\times \$12{,}000=\$1{,}800\).
4. Maturity payment. The payment is \(M=\$80{,}000+\$12{,}000+\$1{,}800=\$93{,}800\).
Check. The $1,800 terminal bonus is 15% of the $12,000 eligible base. The basic guarantee and additions are each included once, giving a final payment of $93,800.
Worked Example: A Base That Includes the Guarantee
Hypothetical policy. The basic guaranteed maturity benefit is $120,000. Simple additions of 1% of that benefit are vested for each completed policy year. In addition, a separate $3,600 addition has already vested. Maturity is 11 years and 7 months after issue. The scale pays 6% below 8 completed years, 12% from 8 through 11 completed years, and 20% from 12 years onward. It specifies an eligible base of the basic benefit plus all vested additions. Calculate the maturity payment, assuming there are no other amounts. The method is to distinguish the rate base from the final benefit total; this avoids omitting the guarantee from the base or adding the base twice to the payment.
1. Completed duration. At 11 years and 7 months, 11 policy years are completed. The applicable rate is 12%, so \(r(11)=0.12\).
2. Vested additions. Each annual simple addition is \(0.01\times \$120{,}000=\$1{,}200\). Additions earned over 11 completed years total \(11\times \$1{,}200=\$13{,}200\). Including the separate vested addition gives \(V=\$13{,}200+\$3{,}600=\$16{,}800\).
3. Eligible base. This scale includes both the basic benefit and all vested additions. Hence \(E=\$120{,}000+\$16{,}800=\$136{,}800\).
4. Terminal bonus. \(T=0.12\times \$136{,}800=\$16{,}416\).
5. Maturity payment. The base components are already the basic benefit and vested additions; the payment is \(M=\$120{,}000+\$16{,}800+\$16{,}416=\$153{,}216\). The eligible base is not added a second time as a separate amount.
Check. The terminal bonus is exactly 12% of $136,800, and the total exceeds that base by the $16,416 bonus. The final payment is $153,216.
Worked Example: Completed Duration and Excluded Cash Dividends
Hypothetical policy. The basic maturity benefit is $90,000. A simple addition of 0.8% of the basic benefit becomes vested for every completed policy year. A further $2,400 addition is vested. The policy matures after 14 years and 11 months. The policyholder also received cash dividends of $500 at the end of each of 10 earlier years. The terminal scale pays 7% below 10 completed years, 11% from 10 through 14, and 17% from 15 onward; it applies only to vested additions. Calculate the maturity payment. The method is to use completed duration and exclude cash already paid from the stated base, avoiding both a boundary error and a dividend double count.
1. Duration and scale rate. Fourteen years and 11 months means 14 completed years, not 15. The applicable rate is 11%, or \(0.11\).
2. Vested additions. Each yearly addition is \(0.008\times \$90{,}000=\$720\). The additions over 14 completed years are \(14\times \$720=\$10{,}080\). Including the additional vested amount gives \(V=\$10{,}080+\$2{,}400=\$12{,}480\).
3. Eligible base and bonus. The eligible base is the vested additions, \(E=\$12{,}480\). The $5,000 in cash dividends already paid is excluded. Thus \(T=0.11\times \$12{,}480=\$1{,}372.80\).
4. Maturity payment. The payment at maturity is \(M=\$90{,}000+\$12{,}480+\$1{,}372.80=\$103{,}852.80\). The earlier cash dividends are not added to this maturity payment.
Check. Applying 11% to $12,480 gives $1,372.80. The policy has not completed 15 years, and no previously paid dividend is counted again. The final maturity payment is $103,852.80.
Common Errors and Checks
The calculation is short, but each input has a different source: policy duration comes from the maturity date and duration definition; the rate comes from the relevant band; and the base comes from the scale wording. Keep these decisions visible in the working. In particular, do not infer an eligible base from the name “terminal bonus.”
- Using elapsed years as completed years. At 14 years and 11 months, a completed-year scale uses 14, not 15. Do not move into the next band before the required anniversary.
- Applying the rate to the wrong amount. If the scale says “a percentage of vested additions,” the eligible base is not automatically the basic benefit or the total maturity benefit.
- Treating the scale as marginal tiers. A scale with one rate for each duration band normally selects one rate for the policy’s duration. Do not apply several band rates to different years unless the terms explicitly require that method.
- Counting paid cash dividends again. A dividend paid before maturity is not an outstanding maturity addition merely because it was generated by the policy.
- Adding the eligible base twice. The base is an input to the bonus calculation. In the final payment, include its components only once as guaranteed benefits or vested additions.
A useful final check is to write the payment as separate lines: basic guaranteed benefit, vested additions, terminal bonus, and any other maturity amount expressly payable. Then verify that the terminal bonus equals the selected rate multiplied by the stated eligible base. This makes a mistaken rate, base, or duplicate amount easier to detect.
Check Your Understanding
For each hypothetical policy, identify the appropriate duration and base before calculating. The answer is shown after each problem.
- A policy has a $75,000 basic maturity benefit and simple vested additions of 0.9% of that benefit for each completed year. It matures after 10 years and 4 months. The scale pays 5% below 10 years, 12% from 10 through 14 years, and 18% from 15 years onward, on vested additions only. There are no other benefits. What is the maturity payment? (Answer: $82,560)
- A $150,000 basic benefit receives simple vested additions of 1.1% of the basic benefit for each completed year. Maturity is at 9 years and 11 months. The scale pays 8% below 10 completed years and 14% from 10 through 14, on additions only. Calculate the payment. (Answer: $166,038)
- A policy has a $100,000 basic maturity benefit and vested additions of 2% of that benefit for each completed year. It matures after 12 years and 3 months. The scale pays 10% of the basic benefit plus vested additions for durations from 10 through 14 completed years. Calculate the payment. (Answer: $136,400)
- A policy with a basic maturity benefit of $80,000 has simple vested additions of 1% of the basic benefit for each completed year and a separate $4,000 vested addition. It matures exactly on its 15th anniversary. Earlier cash dividends total $2,000. The scale pays 16% of vested additions at 15 completed years and excludes cash dividends. What is the maturity payment? (Answer: $98,560)
- A $200,000 basic benefit receives simple vested additions of 0.75% of the basic benefit for each completed year, plus a separate vested addition of $5,000. Maturity is after 14 years and 11 months. The policyholder previously received $2,000 in cash dividends. The scale pays 12% from 10 through 14 completed years on the basic benefit plus vested additions. Calculate the maturity payment. (Answer: $253,120)