Why Crediting Rates and Valuation Rates Must Be Kept Separate
A universal life policy account grows according to the rate credited to the policy, while an insurer values its future obligations using a stated valuation basis. Those rates answer different questions. The crediting rate determines the policyholder’s projected account value; the valuation rate discounts future insurer cash flows. Comparing them carefully reveals an interest margin and can change the reserve measured for an account-related obligation.
The calculations in this tutorial use a deliberately isolated annual model: the account balance is present at the start of each year, no premium, charge, withdrawal, claim, or other cash flow occurs during the year, and interest is credited at year-end. This keeps the interest effect visible. In a full policy projection, other cash flows must be included at their specified times.
An insurer’s dollar interest margin for a year is not simply the difference between two rates: it depends on the balance exposed to those rates. When the same beginning balance supports assets and the credited account, and there are no other cash flows in the year, the year’s interest margin is
A positive result means the assets earn more interest than is credited on that balance for the year. It is an interest margin only; it is not necessarily total policy profit, because mortality costs, expenses, taxes, charges, capital costs, and other cash flows have been deliberately excluded.
Projecting the Account and Measuring the Annual Spread
The calculation must use the account value at the start of the year, not the ending value. Credited interest is applied to that starting balance, so the amount credited during the year is \(AV_tc_t\). If rates vary by year, project the account sequentially using the rate for each year. A rate stated for one year should not be applied to a different period without converting it to a consistent effective rate.
Worked Example: One-Year Interest Margin
A hypothetical policy has an account value of $10,000 at the start of a year. The account is credited an effective annual rate of 4%, while the supporting assets earn an effective annual rate of 6%. There are no other cash flows. Find the ending account value and the insurer’s interest margin for the year.
Method. Project the policy obligation at the credited rate, and calculate asset interest and credited interest separately on the opening account value.
The interest credited to the account is
Therefore, the ending account value is
The assets earn
The interest margin is asset interest less credited interest:
Check. The $200 margin is also the difference between the $10,600 of assets after interest and the $10,400 account obligation at year-end. A common mistake is to multiply the 2% rate spread by the ending account value of $10,400. That would give $208, but it uses a balance that was not exposed for the full year. The correct exposure is the opening balance, so the margin is $200.
For multiple years, annual margins can be added as dollar amounts only if the question asks for the total earned over those years without accumulating earlier margins. If prior margins remain invested, they also earn interest. The following example keeps the account obligation and accumulated asset surplus separate.
Worked Example: Changing Credited Rates Over Two Years
A hypothetical policy begins with an account value of $20,000. Assets supporting the account earn 5% effective annually in each of the next two years. The credited rate is 3% in year 1 and 4% in year 2. Assume the asset surplus created in year 1 remains invested and earns 5% in year 2. Calculate the account value after two years, the asset value after two years, and the resulting interest surplus.
Method. Roll the account forward at the credited rate each year. Separately roll the assets forward at the asset yield. This avoids applying one rate to both sides of the comparison.
After year 1, the account value is
After year 2, the account value is
The assets after year 1 are
At the end of year 2, they are
Thus the asset surplus over the account obligation at the end of year 2 is
Check by annual margins. The first-year margin is
That $400 surplus earns 5% in year 2, becoming $420. The second-year margin on the account balance is
Together, the year-end surplus is \( \$420+\$206=\$626 \), agreeing with the direct asset-minus-account calculation. A common mistake is to add $400 and $206 and report $606; that omits the $20 interest earned on the first-year surplus.
Discounting Account-Related Cash Flows
A reserve is a valuation of future obligations under specified assumptions, not a synonym for the policy account value. In a deterministic model, if a single account-related payment \(C_k\) is due at time \(k\), its present value at time 0 using annual effective valuation rate \(i_v\) is \(C_k/(1+i_v)^k\). With several payments, discount each one to the same valuation date and then add them. If cash flows are contingent or the assumptions are stochastic, the valuation must also reflect the applicable probabilities or scenario assumptions; the simple deterministic calculation alone is not sufficient.
For an account balance with a constant credited rate \(c\) over \(n\) years and no intervening cash flows, the projected account-related payment at time \(n\) is \(AV_0(1+c)^n\). Its present value on a constant annual valuation basis is
This formula is for a single future payment equal to the projected account value, under the stated simplified assumptions. It does not by itself value a death benefit, surrender payment, or any other amount that differs from the account value.
Worked Example: Reserve Effect of a Credited-Rate Spread
A hypothetical policy has an account value of $50,000 now. It is credited 3% for the next year, and the only future obligation considered is payment of the resulting account value at year-end. The valuation rate is 5% effective annually. Assume no other cash flows, decrements, or expenses. Calculate the one-year projected obligation, its present value, and the difference between the current account value and this reserve.
Method. First project the obligation using the credited rate. Then discount that amount using the valuation rate.
The account-related payment at year-end is
The reserve at time 0 is
The account value exceeds this reserve by
The spread check gives the same result:
Check. At the valuation rate, assets of $50,000 grow to $52,500, while the projected account obligation is $51,500. The $1,000 year-end difference discounted at 5% is $952.38. Report money to the nearest cent. A common mistake is to discount $51,500 at the credited rate of 3%, which would simply reverse the account projection and return $50,000. The specified valuation rate is 5%, so it—not the credited rate—must be used for discounting.
A Reliable Calculation Sequence
Keeping the steps separate makes calculations easier to audit, particularly when rates change by year or the cash flow is not paid immediately.
Identify each valuation date, account-value date, and payment date. State whether rates are effective annual rates and which balance is exposed during each period.
Apply each period’s credited rate to the appropriate opening account value. Include other account transactions only if the problem specifies them and their timing.
Use the asset yield for the asset-side calculation. Do not substitute the valuation rate unless the problem explicitly equates them.
Compare asset and credited interest on the same exposed balance, then discount future insurer cash flows on the specified valuation basis.
Reconcile an accumulated surplus to assets less obligations, or verify a one-year reserve comparison with the spread identity. Confirm the rate and timing used for every step.
Common Traps and Practical Interpretation
An interest spread is a rate comparison tied to a balance and a period. An account-related reserve is a present value tied to future obligations and a valuation basis. Treating these as interchangeable can produce a plausible-looking but incorrect answer.
- Using the ending balance for a full-year spread. With no interim transactions, the starting balance is the amount exposed through the year. Apply the rate difference to that balance.
- Using the credited rate to discount. The credited rate projects the account obligation; the stated valuation rate discounts that obligation.
- Confusing actual yield with valuation interest. An assumed asset yield measures asset growth in a projection. A valuation rate is an assumption for present value. They may coincide, but that must be specified.
- Ignoring the accumulation of earlier margins. If a prior surplus remains invested, it earns interest as well as any new annual spread.
- Calling the interest margin total profit. The isolated spread excludes other policy cash flows and risk components unless those have been explicitly included.
These distinctions are useful whenever an account-based policy has a credited rate that differs from the rate used to value insurer obligations. A disciplined calculation identifies the balance, period, cash-flow timing, and rate basis before doing arithmetic. This treatment is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.
Check Your Understanding
For each problem, use the stated annual effective rates and assumptions. Round dollar amounts to the nearest cent where necessary.
- A hypothetical policy has an opening account value of $18,000. It is credited 2.5% for one year, while supporting assets earn 4%. There are no other cash flows. Find the ending account value and the one-year interest margin. (Answer: ending account value $18,450; interest margin $270.)
- An account starts at $12,000. The credited rates are 2% in year 1 and 3% in year 2. Assets earn 4% in each year, and the first-year asset surplus remains invested at 4%. Find the account value and the asset surplus at the end of year 2. (Answer: account value $12,607.20; asset surplus $372.)
- A $20,000 account-related payment is projected to be paid one year from now. The account is credited 6% for that year, and the valuation rate is 4%. Find the projected payment and its present value. (Answer: projected payment $21,200; present value $20,384.62.)
- A valuation requires discounting payments of $5,000 at the end of year 1 and $7,000 at the end of year 2. The annual effective valuation rate is 5%. Find their total present value. (Answer: $11,111.11.)
- A policy has an opening account value of $25,000, earns a credited rate of 3% annually for two years, and has a single account-related payment at the end of year 2. The valuation rate is 5% annually. Find the payment and its present value. (Answer: payment $26,522.50; present value $24,056.69.)