What Is Paid at Maturity?
An equity-linked policy’s fund changes as premiums are allocated, investment returns are credited, and charges are deducted. At maturity, the fund value is a key input to the benefit calculation, but it is not automatically the amount the policyholder receives. The contract may pay the fund alone, or it may promise a minimum maturity amount if the fund is too small.
The first task is therefore to project the fund to the specified maturity date using the contractual timing of cash flows. The second is to apply the maturity benefit provision to that projected value. These are separate calculations: a guarantee does not change the investment account projection unless the contract explicitly says that it does.
The recurrence depends on the stated sequence of transactions. Here, the premium is added before the year’s investment return, while the charge is subtracted after that return. If a contract instead deducts charges monthly, deducts them before investment return, or allocates premiums at a different date, the projection must reflect those terms. A fund projection is not determined by the annual return alone.
In the examples below, investment returns are deterministic values specified for each year; no probability distribution of returns is assumed. There is no separate fixed interest rate used to project the fund. For the benefit calculation, assume the policyholder survives to maturity and satisfies any stated eligibility conditions. No mortality probabilities are needed to calculate the amount payable conditional on maturity eligibility.
Projecting a Fund-Only Maturity Benefit
For a contract that pays the fund alone, the maturity benefit equals the projected fund at the maturity date. This does not mean that the original premium is returned: charges and investment experience affect the amount. It is important to carry the fund forward year by year, rather than apply a single return to total premiums when contributions and charges occur at different times.
Worked Example: Fund-Only Benefit After Three Years
A hypothetical policy receives an allocated premium of $12,000 at the start of year 1. There are no later premiums. At the end of each year, a $200 charge is deducted after investment growth. The annual fund returns are 10% in year 1, −5% in year 2, and 8% in year 3. The contract pays the fund alone at the end of year 3. Assume the policyholder survives to maturity. Returns are deterministic; no return distribution or separate interest rate is assumed.
Method. Apply the annual fund recurrence, using zero premiums after year 1.
At the end of year 1:
At the end of year 2, the year’s return is −5%, so the accumulation factor is \(1-0.05=0.95\):
At the end of year 3, the accumulation factor is \(1+0.08=1.08\):
Because this is a fund-only contract, the maturity benefit is $12,922.00. The result is checked by confirming that each year’s charge is deducted after that year’s return and that no premiums are added after year 1. The common mistake avoided is applying the three-year returns to the original premium as if all charges occurred at maturity.
Applying a Maturity Guarantee
A maturity guarantee sets a minimum amount payable at maturity according to the contract’s terms. One common form pays the greater of the projected fund and a specified guaranteed amount. In that case, calculate the fund first, calculate the guarantee separately, and compare the two. The guarantee may be based on a fixed dollar amount, a stated proportion of premiums, or another contractual definition; it must not be inferred from the fund projection.
A guarantee is not necessarily payable in every circumstance. The contract may require the policy to remain in force to a particular date, or may define how withdrawals affect the guarantee. The examples here state the guarantee and eligibility conditions explicitly. Other conditions must be handled according to the policy wording.
Worked Example: A Fixed Minimum at Maturity
A hypothetical policy begins with an allocated premium of $15,000. It earns −10% in year 1 and 4% in year 2. A $100 charge is deducted at the end of each year, after investment growth. At maturity, if the policyholder survives and the policy is in force, the contract pays the greater of the fund and a fixed guaranteed amount of $15,000. Returns are deterministic, with no probability distribution or separate interest rate assumed.
Step 1: Project the fund. At the end of year 1:
At the end of year 2:
Step 2: Apply the maturity provision. The fund is $13,836 and the guarantee is $15,000, so the payable amount is the greater:
The maturity benefit is $15,000.00. The fund remains $13,836; it is the benefit provision that ensures a larger amount is paid. A common error is to add the guarantee to the fund and report $28,836. That is incorrect because the stated contract pays the greater of the two amounts, not their sum.
Read the Guarantee Base Carefully
A guarantee amount and a fund value can be based on different quantities. For example, the fund may reflect investment returns and charges, while a guarantee may be defined as a percentage of gross premiums. Do not substitute the fund for the stated guarantee base, or reduce that base for charges unless the contract says to do so. Also check whether premiums are counted when paid, allocated, or subject to some other eligibility rule.
Worked Example: Guarantee Based on Gross Premiums
A hypothetical three-year policy receives premiums of $5,000 at the start of each of the three years. Each year, the fund earns that year’s return and then a $100 charge is deducted. The returns are 4%, −10%, and −20%, respectively. At maturity, the policyholder must be alive and the contract in force. The benefit is the greater of the fund and 95% of total gross premiums paid. Returns are deterministic; no probability distribution or separate interest rate is assumed.
Step 1: Project year 1.
Step 2: Add the second premium, then project year 2.
Step 3: Add the third premium, then project year 3.
Step 4: Calculate the guarantee using its stated base. Total gross premiums are \(5{,}000+5{,}000+5{,}000=15{,}000\). Thus:
The fund is $11,092, below the guarantee of $14,250. Therefore, the maturity benefit is $14,250.00. The result is checked against both independently calculated values: the projected account is $11,092, while 95% of gross premiums is $14,250. The common mistake avoided is applying 95% to the fund, or subtracting the $300 of charges from gross premiums before calculating a guarantee explicitly defined on gross premiums.
A Reliable Calculation Sequence
The following sequence keeps the fund projection separate from the benefit selection and makes timing assumptions visible. It is useful even when the projection includes more years, changing premiums, or a mixture of positive and negative returns.
Identify the maturity date, survival or in-force requirement, and any other condition that determines eligibility for payment.
Record when premiums are added, when returns apply, and when charges are deducted. Use the contract’s order, not an assumed order.
Carry the fund forward one period at a time, using the return and transactions for each period.
Use the stated guarantee base and apply any contractual adjustments, such as those for withdrawals, only when specified.
For a fund-only contract, pay the fund. For a contract that promises the greater of fund and guarantee, compare the two amounts and select the larger.
Common Exam Traps
- Using the wrong timing. A premium added at the start of a year earns that year’s return under the recurrence used here. An end-of-year premium would not earn that same return.
- Applying a charge in the wrong place. A charge deducted after investment growth is not equivalent to one deducted before growth. Follow the timing given.
- Stopping at the fund value. A maturity guarantee may change the benefit payable even though it does not change the projected fund.
- Adding the fund and guarantee. This is wrong when the contract promises the greater of the two. Identify the exact payment wording before selecting a formula.
- Changing the guarantee base. If the guarantee is a percentage of gross premiums, calculate it from gross premiums, not from the post-charge fund.
- Ignoring maturity eligibility. A maturity benefit generally depends on the policy reaching its specified maturity under the contract’s conditions. Do not apply the maturity amount to a different event without a contractual basis.
These distinctions matter because the projected account and the contractual benefit answer different questions. The fund projection describes the account after investment performance and charges. The maturity benefit describes the amount the insurer must pay under the policy terms. Keeping those calculations separate is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.
Check Your Understanding
For each problem, assume the policyholder survives to maturity and satisfies the stated in-force conditions. Returns are deterministic; no return distribution or separate interest rate is assumed. Apply charges at the end of each year after investment growth unless stated otherwise.
- A fund starts at $8,000, earns 6% in each of two years, and has a $150 charge deducted at each year-end. The contract pays the fund alone. What is the maturity benefit? (Answer: $8,679.80)
- A $12,000 premium is allocated at the start of year 1. Returns are −8% in year 1 and 5% in year 2, with a $100 charge at each year-end. The maturity benefit is the greater of the fund and a fixed $11,500 guarantee. What is payable? (Answer: $11,500.00)
- A policy receives $4,000 at the start of year 1 and $3,000 at the start of year 2. Returns are 5% and 0%, with a $50 charge at each year-end. The maturity guarantee is 90% of gross premiums, and the benefit is the greater of fund and guarantee. What is payable? (Answer: $7,100.00)
- A $10,000 fund earns −15% in year 1 and 10% in year 2. A $100 charge is deducted at each year-end. Compare the fund-only benefit with a contract that instead pays the greater of the fund and a $9,500 maturity guarantee. (Answer: Fund-only benefit $9,140.00; guaranteed-contract benefit $9,500.00)
- A policy receives $6,000 at the start of year 1 and $2,000 at the start of year 2. The returns are 3% and −12%, with a $75 charge at each year-end. The guarantee is 90% of total gross premiums, and the contract pays the greater of fund and guarantee. Calculate both amounts and the maturity benefit. (Answer: Fund $7,057.40; guarantee $7,200.00; maturity benefit $7,200.00)