Bonus Declarations On Paid-Up Policies

Paid-Up Status and Future Bonus Declarations

A policy is paid-up when its required regular premiums have ceased, while a reduced amount of insurance remains in force under the contract. Paid-up status means the projection must not include future premiums. It does not, by itself, determine whether future reversionary bonuses will be declared or what amount those bonuses will use as their base.

For a participating policy, a reversionary bonus declared while the policy is eligible generally adds to its guaranteed benefit under the contract. A projection therefore starts with the benefit already in force, identifies the base specified for future declarations, and applies only the assumed declarations. The result is conditional on those declarations being made and on the policy remaining eligible and in force.

Definition: Let $S_{\mathrm{pu}}$ be the paid-up basic sum assured and $V_0$ the vested reversionary additions already attached to the policy at the projection date. The current guaranteed benefit is $B_0=S_{\mathrm{pu}}+V_0$, provided the contract pays those amounts together on the benefit being projected. A future reversionary bonus increases that benefit when declared; no future premium is included in this projection.

The contract’s bonus terms determine the bonus base. Depending on those terms, a declaration may be calculated using the paid-up basic sum assured, the original sum assured, or a benefit amount that already includes vested additions. These bases are not interchangeable. In particular, do not assume that an existing addition is part of the base merely because it is included in the current guaranteed benefit.

A declaration rate is also not necessarily a promise that the same rate, or any rate, will be declared in future years. Unless future declarations are contractually guaranteed, a numerical projection is a scenario: it answers what the benefit would be if the specified declarations occur.

Compound and Simple Bonus Projections

In a compound reversionary bonus projection, each new addition is included in the base for a later declaration if the stated bonus terms say the rate applies to the current guaranteed benefit. If the annual rate is $r$ and the benefit at the start is $B_0$, then after $k$ declarations the recurrence is $B_k=B_{k-1}(1+r)$. This form is appropriate only when each declaration is a percentage of the then-current benefit.

In a simple bonus projection, the annual addition is calculated on a fixed base, such as the paid-up basic sum assured. Earlier additions do not themselves earn further additions under that scale. If the annual simple rate is $r$ on fixed base $S_{\mathrm{pu}}$, then $B_n=B_0+nrS_{\mathrm{pu}}$. A fixed dollar bonus per unit of sum assured follows the same additive logic, with the annual dollar addition calculated from the specified unit base.

\begin{aligned} \text{Compound on current benefit:}\quad &B_k=B_{k-1}(1+r), \qquad B_n=B_0(1+r)^n,\\ \text{Simple on fixed base:}\quad &B_k=B_{k-1}+rS_{\mathrm{pu}}, \qquad B_n=B_0+nrS_{\mathrm{pu}}. \end{aligned}

These formulas describe different declaration rules. A percentage rate alone does not tell you whether the bonus compounds: the contract or problem must specify the base. For a rate quoted as a dollar amount per $1,000, first determine which sum assured the rate applies to, then calculate the annual addition in dollars.

Derivation: Under a compound scale, a declaration adds $rB_{k-1}$ to the benefit already in force. Thus $B_k=B_{k-1}+rB_{k-1}=(1+r)B_{k-1}$. Repeated substitution gives $B_1=B_0(1+r)$, $B_2=B_0(1+r)^2$, and, after $n$ declarations, $B_n=B_0(1+r)^n$. Under a simple scale, each year instead adds the same amount $rS_{\mathrm{pu}}$, so summing $n$ equal additions gives $B_n=B_0+nrS_{\mathrm{pu}}$.

Worked Projections

Worked Example: Compound Declarations After Premiums Cease

A hypothetical policy has a paid-up basic sum assured of $80,000 and $6,000 of vested reversionary additions. The contract scenario specifies a 2% compound bonus at each of the next three anniversaries, calculated on the guaranteed benefit immediately before each declaration. Find the projected benefit after the third declaration. Assume a deterministic sequence of declarations and continued eligibility. Interest is 0% for this undiscounted benefit projection; mortality is not modeled because the calculation is conditional on the policy remaining in force through all three anniversaries. No future premiums are paid.

Method. Add the paid-up basic sum assured and existing vested additions to obtain the starting benefit:

B_0=\$80{,}000+\$6{,}000=\$86{,}000.

The first declaration adds $0.02(\$86{,}000)=\$1{,}720$, giving $B_1=\$87{,}720$. The second adds $0.02(\$87{,}720)=\$1{,}754.40$, giving $B_2=\$89{,}474.40$. The third adds $0.02(\$89{,}474.40)=\$1{,}789.488$, giving $B_3=\$91{,}263.888$.

Equivalently, $B_3=\$86{,}000(1.02)^3=\$91{,}263.888$. Rounded to the nearest cent, the projected guaranteed benefit is $91,263.89. The total new additions are $\$91{,}263.888-\$86{,}000=\$5{,}263.888$, which agrees with the sum of the three annual additions before rounding. The common mistake avoided here is calculating all three bonuses on the original $86,000 when the stated scale compounds on the current benefit.

Worked Example: Simple Bonuses on the Paid-Up Basic Sum Assured

A hypothetical policy is paid up with a basic sum assured of $120,000 and $9,000 of vested additions. It remains eligible for four annual simple reversionary bonuses of 1.5% of the paid-up basic sum assured. Calculate the benefit after the fourth declaration. Assume the four declarations occur as stated and the policy remains in force. Interest is 0% because no present value is required; mortality is not modeled. The bonus sequence is deterministic, and no future premiums are paid.

Method. First find the current guaranteed benefit: $B_0=\$120{,}000+\$9{,}000=\$129{,}000$. The annual addition is fixed at $0.015(\$120{,}000)=\$1{,}800$, because the stated base is the paid-up basic sum assured, not the current benefit.

After one declaration, $B_1=\$129{,}000+\$1{,}800=\$130{,}800$. After two, $B_2=\$130{,}800+\$1{,}800=\$132{,}600$. After three, $B_3=\$132{,}600+\$1{,}800=\$134{,}400$. After four, $B_4=\$134{,}400+\$1{,}800=\$136{,}200$.

The check using the simple-bonus formula is $B_4=\$129{,}000+4(0.015)(\$120{,}000)=\$136{,}200$. Thus the projected benefit is $136,200.00. The common mistake avoided is applying 1.5% to the increasing total benefit, which would incorrectly turn a simple scale into a compound one.

Worked Example: Applying a Per-Unit Rate to the Paid-Up Base

A hypothetical policy originally had a basic sum assured of $150,000. Following cessation of premiums, its paid-up basic sum assured is $90,000, and it has $4,500 of vested additions. The stated scale declares $18 for each $1,000 of paid-up basic sum assured at each of the next five anniversaries. Additions are simple, not compounded. Find the projected benefit after five declarations. Assume deterministic declarations and continued in-force eligibility. Interest is 0% for this benefit projection; mortality is not modeled. No future premiums are paid.

Method. The current guaranteed benefit is $B_0=\$90{,}000+\$4{,}500=\$94{,}500$. The applicable base is $90,000, or $90$ units of $1,000. Therefore, each annual addition is $90(\$18)=\$1{,}620$.

The five additions are each $1,620, so their total is $5(\$1{,}620)=\$8{,}100$. The projected benefit is $B_5=\$94{,}500+\$8{,}100=\$102{,}600$. As a component check, this equals the $90,000 paid-up basic sum assured, plus $4,500 already vested, plus $8,100 of projected additions.

The projected benefit is $102,600.00. Using the original $150,000 sum assured would produce $150(\$18)=\$2{,}700$ per year and an incorrect total of $\$94{,}500+5(\$2{,}700)=\$108{,}000$. The correction is to follow the stated base: this scale applies to the paid-up sum assured, not the original sum assured.

Checks and Common Traps

A reliable projection keeps three quantities distinct: the paid-up basic sum assured, the additions already vested at the valuation date, and the additions assumed in future declarations. The starting benefit may include the first two, but a future bonus base may include only one of them. Set out the base in words before substituting numbers.

Establish the policy status.
Use the paid-up benefit in force and include no future premiums. State that the policy is assumed to remain eligible for the declarations being projected.

Identify the starting benefit.
Add existing vested additions only when they form part of the benefit being projected.

Read the bonus basis and method.
Determine whether the scale is compound on the current benefit, simple on a fixed sum assured, or a stated dollar amount per unit.

Apply each declaration once.
Calculate the addition on the specified base, update the benefit, and use the updated benefit for the next declaration only if the scale compounds.

Check the result.
Reconcile the final benefit to the starting benefit plus all new additions, and label the projection as conditional if future declarations are not guaranteed.

The most common errors are treating every percentage scale as compound, using the original rather than paid-up sum assured without support from the terms, or adding the same vested additions twice. Another error is presenting assumed future declarations as guaranteed merely because earlier declarations have vested. A projection of future declarations is not itself a declaration.

This distinction matters when assessing a paid-up policy’s future contractual benefit. Premium cessation changes the in-force basic amount and removes future premium cash flows, but it does not authorize an analyst to invent a bonus entitlement or silently change the bonus base. A sound projection follows the specified basis, clearly separates existing guarantees from assumed future additions, and makes no claim about declaration certainty beyond the stated terms.

Check Your Understanding

For each problem, assume the policy remains eligible and in force through the stated declarations. No future premiums are paid; no discounting or mortality calculation is required.

A paid-up basic sum assured of $75,000 has $3,000 of existing additions. Four simple annual bonuses equal 1.2% of the paid-up basic sum assured. What is the benefit after the fourth declaration? (Answer: $81,600.00)
A policy has a $50,000 paid-up basic sum assured and $2,000 of vested additions. Two annual compound bonuses of 3% apply to the current guaranteed benefit. Find the benefit after the second declaration. (Answer: $55,166.80)
A paid-up sum assured of $80,000 has $5,000 of existing additions. The simple annual scale is $12 per $1,000 of paid-up sum assured for three years. Find the final benefit. (Answer: $87,880.00)
A current guaranteed benefit is $102,000. Two compound declarations of 1.5% apply to that current benefit and its successive values. Calculate the benefit after the second declaration. (Answer: $105,082.95)
A policy originally had a $120,000 sum assured, now reduced to a paid-up basic sum assured of $72,000, with $2,400 of vested additions. The simple scale is $20 per $1,000 of paid-up sum assured for four declarations. What is the projected benefit? (Answer: $80,160.00)

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