Deducting Monthly Policy Charges

Monthly Charges and the Account Balance

A universal life policy account can be subject to charges each month. A mortality charge is commonly determined from a stated rate and the policy's net amount at risk; an expense charge may also be deducted. The calculation requires careful attention to the rate's units and to the order of account transactions. A small timing or unit error can materially change a projected account value.

This tutorial focuses on the arithmetic of assessing and deducting those charges. Every example is hypothetical, with its monthly crediting and deduction timing stated explicitly. The monthly mortality charge rate in these examples is a contract rate per $1,000 of net amount at risk; it is not a probability of death.

Definition: Let $A_{t-1}$ be the account value at the start of month $t$, $j_t$ the effective interest rate credited for that month, $N_t$ the net amount at risk used for the month's charge, $\alpha_t$ the mortality charge rate in dollars per $1,000 of net amount at risk, and $E_t$ the scheduled monthly expense charge. If interest is credited before charges are deducted, the amount available for the deductions is $B_t=A_{t-1}(1+j_t)$. The scheduled mortality charge is $M_t=\alpha_t N_t/1{,}000$, and total scheduled charges are $C_t=M_t+E_t$.

If $B_t$ is at least $C_t$, the full scheduled charge can be deducted and the closing account value is $B_t-C_t$. If $B_t$ is less than $C_t$, this simple account projection does not allow a negative account value: the amount available is deducted, the closing value is zero, and the shortfall is the part of the scheduled charges that could not be collected from the account. How a contract treats that shortfall is outside this calculation.

\text{Actual deduction}_t=\min(B_t,C_t), \qquad A_t=\max(B_t-C_t,0), \qquad \text{Shortfall}_t=\max(C_t-B_t,0).

These expressions describe a specified transaction order, not a universal rule for every contract. If a problem places premiums, interest, or charges at different points in the month, follow that stated order. In particular, do not apply a charge before interest merely because both transactions occur in the same month.

Why the Recurrence Works

The account recurrence follows directly from the cash-flow sequence. Under the stated convention, the opening account first earns interest $A_{t-1}j_t$, making the amount available $A_{t-1}+A_{t-1}j_t=A_{t-1}(1+j_t)$. Charges are then taken from that amount. If they fit, subtracting them gives the closing value; if they do not fit, the account can supply only the available amount.

A_t= \begin{cases} A_{t-1}(1+j_t)-C_t, & C_t\leq A_{t-1}(1+j_t),\\ 0, & C_t>A_{t-1}(1+j_t). \end{cases}

Equivalently, the shortfall is positive only when scheduled charges exceed the amount available. This distinction matters: a scheduled charge is the amount called for by the charge formula, while an actual deduction cannot exceed available account value in this projection. A zero closing account value therefore does not mean the scheduled charges were fully collected.

Worked Example: Projecting Three Months of Charges

A hypothetical policy opens month 1 with an account value of $160. The account earns 0.4% effective interest each month, credited before charges. The monthly mortality charge rate is $0.16 per $1,000 of net amount at risk, and the monthly expense charge is $3.50. The net amounts at risk in months 1, 2, and 3 are $25,000, $40,000, and $50,000. Find the account value after each month's charges and at the end of month 3. Assume no premiums or other transactions. The method is a month-by-month recurrence; it avoids treating the monthly rate as a percentage of the full net amount at risk.

Month 1. The amount available after interest is $160(1.004)=160.64$. The mortality charge is $(25{,}000/1{,}000)(0.16)=25(0.16)=4.00$. Total scheduled charges are $4.00+3.50=7.50$. Since $160.64 exceeds $7.50, the full amount is deducted, leaving $160.64-7.50=\$153.14$.

Month 2. The amount available is $153.14(1.004)=153.75256$. The mortality charge is $(40{,}000/1{,}000)(0.16)=40(0.16)=6.40$. Total scheduled charges are $6.40+3.50=9.90$. The closing value is $153.75256-9.90=\$143.85256$.

Month 3. The amount available is $143.85256(1.004)=144.42797024$. The mortality charge is $(50{,}000/1{,}000)(0.16)=50(0.16)=8.00$. Total scheduled charges are $8.00+3.50=11.50$. The closing value is $144.42797024-11.50=\$132.92797024$.

Check and result. Expanding the recurrence gives $160(1.004)^3-7.50(1.004)^2-9.90(1.004)-11.50=161.92769024-28.99972=132.92797024$, agreeing with the month-by-month calculation. Rounded only at the final step, the month-end values are $153.14, $143.85, and $132.93. A common mistake is to deduct $0.16 times $25,000, rather than first converting $25,000 to 25 units of $1,000; that would produce an implausibly large charge and uses the rate's units incorrectly.

When Scheduled Charges Exceed the Available Value

A sufficient account value allows the full charge to be collected. When the amount available is smaller than the scheduled charges, calculate the difference explicitly rather than allowing the account to become negative. The following example separates three quantities that are easy to confuse: the amount available, the actual deduction, and the shortfall.

Worked Example: Checking Whether Charges Can Be Fully Deducted

A hypothetical policy opens a month with $28. The account earns 0.25% effective interest for that month, credited before charges. The mortality charge rate is $0.30 per $1,000 of net amount at risk, the net amount at risk is $40,000, and the monthly expense charge is $5. Find the amount available, the scheduled charges, the actual deduction, any shortfall, and the closing value. The method is to compare available value with total scheduled charges before deciding whether the deduction is complete; this avoids incorrectly setting a positive residual account value to zero.

The amount available after interest is $28(1.0025)=\$28.07$. The mortality charge is $(40{,}000/1{,}000)(0.30)=40(0.30)=\$12.00$. Total scheduled charges are $12.00+5.00=\$17.00$. Because $28.07 is greater than $17.00, the actual deduction is the full $17.00 and the shortfall is zero.

The closing value is $28.07-17.00=\$11.07$. The check $11.07+17.00=28.07$ confirms that the available amount is fully accounted for. To the cent, the results are: $28.07 available, $17.00 scheduled and actually deducted, no shortfall, and an $11.07 closing value.

Worked Example: Recording a Charge Shortfall

A hypothetical policy opens a month with $42. It earns 0.2% effective monthly interest before deductions. The mortality charge rate is $0.25 per $1,000 of net amount at risk, with a $100,000 net amount at risk in month 1 and $80,000 in month 2. The monthly expense charge is $8 in each month. No other transactions occur. Calculate the actual deduction, shortfall, and closing value for each month. The method is to apply the account-value cap separately in each month; it avoids carrying a negative balance into the next month's interest calculation.

Month 1. The amount available is $42(1.002)=\$42.084$. The mortality charge is $(100{,}000/1{,}000)(0.25)=100(0.25)=\$25.00$, so total scheduled charges are $25.00+8.00=\$33.00$. The available value is sufficient. The actual deduction is $33.00, the shortfall is zero, and the closing account value is $42.084-33.00=\$9.084$.

Month 2. Interest is credited only on the positive opening account value: $9.084(1.002)=\$9.102168$ is available. The mortality charge is $(80{,}000/1{,}000)(0.25)=80(0.25)=\$20.00$. Total scheduled charges are $20.00+8.00=\$28.00$, which exceeds the available value. The actual deduction is therefore $9.102168, the closing value is zero, and the shortfall is $28.00-9.102168=\$18.897832$.

Check and result. In month 2, actual deduction plus shortfall is $9.102168+18.897832=\$28.00$, exactly the scheduled charge. Rounded to cents only at the final step, month 1 closes at $9.08; in month 2, $9.10 is available and actually deducted, the shortfall is $18.90, and the closing value is $0.00. The unrounded values are retained for the month-to-month calculation.

Timing, Units, and Rounding Checks

A useful way to organize a monthly calculation is to keep a separate line for the account value entering the month, the amount after interest, each charge, and the closing value. This makes it easier to locate an error than trying to calculate a multi-month projection in one expression.

Apply the stated timing.
Calculate the account value after any transactions that precede charges. In the examples here, monthly interest is credited first: $B_t=A_{t-1}(1+j_t)$.

Calculate each scheduled charge.
For a rate stated per $1,000, calculate $(N_t/1{,}000)\alpha_t$, then add the stated expense charge.

Compare before subtracting.
If $B_t\geq C_t$, deduct all charges. If $B_t<C_t$, record an actual deduction of $B_t$, a shortfall of $C_t-B_t$, and a zero closing account value.

Carry full precision through the projection.
Unless the problem specifies a rounding convention, retain unrounded values between months and round the reported money amounts at the end.

The most common exam traps are applying a per-$1,000 rate to the entire net amount at risk, confusing a scheduled charge with the amount the account can actually fund, and changing the order of interest and charges. Another error is rounding each month before projecting the next one. If a problem explicitly specifies monthly rounding, use it; otherwise, premature rounding can alter the final answer.

Key takeaway: For each month, determine the amount available under the stated transaction order, calculate mortality and expense charges in their stated units, and compare the two before recording the deduction. A charge shortfall is not a negative account balance.

Check Your Understanding

For each problem, follow the timing and charge conventions stated in its data. Round dollar answers to the nearest cent.

A hypothetical policy opens the month with $80, earns 0.3% effective monthly interest before charges, and has a $0.20 mortality charge rate per $1,000 of a $30,000 net amount at risk. The expense charge is $4. Find the amount available and closing account value. (Answer: $80.24 available; $70.24 closing value.)
A policy account starts at $55 and earns 0.5% monthly interest before deductions. Its mortality charge rate is $0.25 per $1,000 of net amount at risk, the net amount at risk is $40,000, and the expense charge is $7. Find the scheduled charges and closing value. (Answer: $17.00 scheduled charges; $38.28 closing value.)
An account starts month 1 at $100 and earns 0.2% monthly interest before charges in each of two months. The mortality charge rate is $0.12 per $1,000 of net amount at risk; the net amounts at risk are $50,000 and $60,000. The expense charge is $5 per month. Find the closing value after month 2. (Answer: $77.18.)
A policy account starts a month at $20 and earns 1% monthly interest before charges. The mortality charge rate is $0.30 per $1,000 of a $50,000 net amount at risk, and the expense charge is $8. Find the actual deduction, shortfall, and closing value. (Answer: $20.20 actual deduction; $2.80 shortfall; $0.00 closing value.)
An account starts at $300 and earns 0.3% monthly interest before charges for three months. The mortality charge rate is $0.10 per $1,000 of net amount at risk; monthly net amounts at risk are $100,000, $120,000, and $140,000. The expense charge is $9 each month. Find the month 3 closing value, retaining full precision between months. (Answer: $239.53.)

What You'll Learn