Pro Rata Cancellation Calculations

Introduction

When a policy is canceled before its scheduled expiration, the insurer may return the portion of the term premium associated with coverage that will not be provided. Under a pro rata cancellation, that portion is allocated in direct proportion to the unused part of the policy term. The calculation is straightforward once the effective cancellation date, the policy term, and the premium eligible for return are identified.

The key distinction is between the return premium credit and the cash refund. The credit is calculated from unused coverage; the cash refund also depends on how much premium the policyholder has paid and whether any premium remains due. This tutorial is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Definition: A pro rata cancellation returns the same fraction of eligible term premium as the fraction of the policy term that remains unused. If $P$ is the eligible premium for a term of $N$ days, and coverage has been provided for $n$ days, the unused-term return premium is $P(N-n)/N$. This calculation assumes a uniform allocation of premium over the term and no separate contractual adjustment to the amount returned.

The Pro Rata Calculation

Let $P$ be the premium eligible for return, $N$ the total number of days in the policy term, and $n$ the number of covered days through the effective cancellation time. The number of unused days is $N-n$. On a pro rata basis, the premium per term-day is $P/N$, so the return premium is the daily premium multiplied by the unused days.

\text{Return premium} = P\left(\frac{N-n}{N}\right)

The corresponding earned premium is the fraction associated with coverage already provided:

\text{Earned premium} = P\left(\frac{n}{N}\right)

These formulas require that $0 \leq n \leq N$, that the term is measured consistently, and that the premium being prorated is eligible for return. For example, if a contract specifies that a particular charge is not refundable, that charge should not be included in $P$ as though it were ordinary pro rata premium. The contract and the stated problem conditions determine the applicable premium and day-count convention.

Why the Formula Works

Pro rata allocation treats each day of the term as carrying an equal share of the eligible premium. Each day therefore corresponds to $P/N$ of premium. For $N-n$ unused days, the total associated premium is $(N-n)(P/N)$, which gives the return formula. Similarly, $n$ days of coverage account for $n(P/N)$ of earned premium.

P\left(\frac{N-n}{N}\right) + P\left(\frac{n}{N}\right) = P\left(\frac{N-n+n}{N}\right) = P

Thus, when the same eligible premium is split between covered and unused time, earned premium plus return premium equals the original term premium. This identity is a useful check on the calculation. The method does not claim that every day has identical actual claim costs; it is a contractual or accounting allocation rule that assumes uniform earning over the stated term.

Set the term and premium basis.
Identify the policy term, its total duration $N$, and the amount $P$ that is eligible for pro rata return.

Count covered and unused time.
Use the effective cancellation time and the stated day-count convention to determine $n$ and $N-n$. Do not count a day twice or omit it.

Calculate the return credit.
Multiply $P$ by the unused fraction $(N-n)/N$. Calculate earned premium separately as a check if useful.

Determine the cash settlement.
Compare the earned premium with amounts paid. A return credit is not automatically the cash refund when premium is unpaid or paid in installments.

Worked Calculations

Worked Example: Cancellation Effective August 1

A hypothetical policy covers the 365-day period from January 1 through December 31, 2025. It has an eligible term premium of $3,650 and is canceled effective August 1, so coverage ends at the close of July 31. Find the return premium credit and verify it using earned premium.

Method. Count the days of coverage through July 31. Because the cancellation is effective August 1, August 1 is not a covered day. January through July contain $31+28+31+30+31+30+31=212$ days. The term has 365 days, so unused time is $365-212=153$ days.

The premium per day is $3{,}650/365=\$10$. Therefore:

\text{Return premium} = \$3{,}650\left(\frac{153}{365}\right) = \$10(153) = \$1{,}530

Earned premium provides a check:

\text{Earned premium} = \$3{,}650\left(\frac{212}{365}\right) = \$10(212) = \$2{,}120

The amounts reconcile: $\$1{,}530+\$2{,}120=\$3{,}650$. The return premium credit is $1,530.00. This example avoids counting August 1 as a covered day when the stated cancellation time ends coverage at the close of July 31.

Worked Example: Cancellation With an Unpaid Premium Balance

A hypothetical 180-day policy has an eligible term premium of $1,440. It is canceled after 75 covered days. The policyholder has paid $900 toward the premium. Find the pro rata return credit and the cash refund after applying the credit to any unpaid premium.

Method. The unused term is $180-75=105$ days. The daily premium is $\$1{,}440/180=\$8$. Thus the return premium credit is:

\text{Return premium} = \$1{,}440\left(\frac{105}{180}\right) = \$8(105) = \$840

The earned premium for 75 covered days is:

\text{Earned premium} = \$1{,}440\left(\frac{75}{180}\right) = \$8(75) = \$600

The unpaid balance on the original premium is $\$1{,}440-\$900=\$540$. The $840 return credit first settles that $540 balance. The amount remaining as a cash refund is $\$840-\$540=\$300$.

Check the settlement another way: the policyholder paid $900, while $600 is earned, so the net overpayment is $\$900-\$600=\$300$. Both methods give a $840.00 return credit and a $300.00 cash refund. The common error is to report the credit itself as the cash refund without accounting for the unpaid $540.

Worked Example: Cancellation Effective October 1 With Partial Payment

A hypothetical policy covers January 1 through December 31, 2025, has an eligible term premium of $2,920, and is canceled effective October 1. Assume coverage ends at the close of September 30. The policyholder has paid $2,500. Calculate the return premium credit and the cash refund after settling the earned premium.

Method. January through September contain $31+28+31+30+31+30+31+31+30=273$ covered days. The unused time is $365-273=92$ days. The daily premium is $\$2{,}920/365=\$8$.

The return premium credit is:

\text{Return premium} = \$2{,}920\left(\frac{92}{365}\right) = \$8(92) = \$736

The earned premium is:

\text{Earned premium} = \$2{,}920\left(\frac{273}{365}\right) = \$8(273) = \$2{,}184

The amount still unpaid is $\$2{,}920-\$2{,}500=\$420$. Applying the $736 return credit to that balance leaves a cash refund of $\$736-\$420=\$316$. As a check, payments exceed earned premium by $\$2{,}500-\$2{,}184=\$316$. The result is a $736.00 return credit and a $316.00 cash refund.

Common Errors and Practical Checks

A pro rata calculation is simple, but small interpretation errors can change the result. First settle exactly when coverage ends and how the term is counted. In a date-based problem, follow the stated effective date convention; in a day-count problem, use the given number of covered days. Do not substitute a calendar-year fraction for an explicitly stated policy-day fraction.

Second, keep the return credit separate from the account settlement. If the full term premium has been paid, the cash refund ordinarily equals the return credit under the assumptions used here. If only part has been paid, some or all of the credit may instead extinguish the unpaid balance. An equivalent settlement check is:

\text{Net cash refund} = \text{amount paid} - \text{earned premium}

This expression gives a refund when positive; if it is negative, the policyholder still owes the magnitude of the shortfall, subject to the contract and billing terms. It follows because the final account should retain payment equal to the premium earned for coverage provided.

Using elapsed time for the return. $P(n/N)$ is earned premium, not return premium. The return fraction is $(N-n)/N$.
Calling the credit the cash refund. First account for unpaid premium or compare payment already made with earned premium.
Changing the stated premium basis. Apply the formula only to the amount identified as eligible for pro rata return.
Ignoring the cancellation boundary. A cancellation effective at the start of a day generally means that day is not covered; use any different convention explicitly provided in the problem.

Key takeaway: Calculate pro rata return premium from the unused fraction of eligible term premium. Then reconcile that credit with the premium earned and paid; the credit and the cash refund are not necessarily the same amount.

Check Your Understanding

For each problem, use the stated term and cancellation convention. Amounts are rounded to the nearest cent if needed.

A hypothetical 240-day policy has an eligible premium of $1,200 and is canceled after 90 covered days. Find the unused days and return premium credit. (Answer: 150 unused days; $750.00 return credit.)
A hypothetical policy has a 365-day term and a $2,190 eligible premium. It is canceled after 250 covered days. The policyholder has paid $1,700 and there are no other charges. Find the return credit and the cash refund after settling earned premium. (Answer: $690.00 return credit; $200.00 cash refund.)
A fully paid hypothetical 120-day policy has an eligible premium of $960 and is canceled after 45 covered days. Find the earned premium and return credit, and verify that they sum to the term premium. (Answer: $360.00 earned; $600.00 return credit; total $960.00.)
A hypothetical policy covers January 1 through December 31, 2025, with a $3,650 eligible premium. It is canceled effective July 1, with coverage ending at the close of June 30. Find the covered days, unused days, and return credit. (Answer: 181 covered days; 184 unused days; $1,840.00 return credit.)
A hypothetical 240-day policy has a $1,800 eligible premium and is canceled after 160 covered days. The policyholder has paid $1,500. Find the return credit, unpaid balance, and cash refund after applying the credit. (Answer: $600.00 return credit; $300.00 unpaid balance; $300.00 cash refund.)

What You'll Learn