What a Refinance Payoff Measures
When an existing loan is replaced, the old lender must receive the amount required to discharge the old obligation on the settlement date. That amount is not necessarily the outstanding balance shown on a statement from an earlier date. Interest may have accrued since then, and the loan contract may specify a prepayment penalty or discharge charge. A credit, such as a payment already received but not yet reflected in the statement, may reduce the amount due.
The calculation is a settlement-date accounting exercise. First identify what the stated balance represents and its date. Then carry that balance to the date of discharge under the applicable interest convention. Finally, add or subtract the other amounts that the settlement terms require. The payoff is distinct from the total cost of refinancing: costs paid to other parties are not part of the old lender’s payoff unless they are explicitly included in the amount needed to discharge that loan.
This topic is aligned with the SOA Exam FM (Financial Mathematics) syllabus. The key is not to add every number in a settlement statement automatically: each item must be classified by date, purpose, and whether it is already included in another amount.
Set the Balance Date and Settlement Date
Let \(B\) be the old loan’s balance immediately after the most recent payment date, and let the refinance payoff date occur later. If no payment or other balance-changing transaction occurs between those dates, the balance must be accumulated to the payoff date. The accumulation factor depends on the loan’s stated interest convention. For example, if the contract specifies a periodic rate \(j\), and \(r\) full periods pass, the accumulated balance is \(B(1+j)^r\). For a different accrual convention, use that convention instead; do not assume that a monthly rate, daily rate, or fractional-year effective rate can be substituted for another without justification.
If the payoff occurs exactly on a payment date, determine whether the quoted balance is immediately before or immediately after that payment. A post-payment balance on that date needs no additional interest for the elapsed time since that date. A balance immediately before the payment may include an installment due on that date, so it cannot be treated as a post-payment balance.
Assembling the Settlement Amount
Use a settlement ledger so that each component appears once. A general structure is:
The contract determines which balance is used as the penalty base. A penalty might be a percentage of principal outstanding on the payoff date, a percentage of principal immediately before accrued interest, or a specified dollar amount. These are different rules. Read the description literally, and do not infer the penalty base from the fact that interest is also due.
A charge should be included only if it is part of the amount required to discharge the old loan or is explicitly included in the requested payoff. A fee for a separate refinancing service is not automatically an old-loan settlement charge. Likewise, a credit should be subtracted only if it applies to the payoff and has not already reduced the stated balance.
Record its date and whether it is before or after any payment on that date. Check whether it is a principal balance, a balance including accrued interest, or a payoff quote.
Use the stated rate convention and elapsed period. Add only interest that has accrued after the balance date and is not already included.
Calculate any penalty on the base specified by the contract. Add applicable discharge charges and subtract applicable credits.
Check signs, dates, and inclusion. Confirm that no payment, interest amount, penalty, or charge has been counted twice.
Why the Accrued-Balance Step Works
Suppose the balance immediately after a payment is \(B\), and the loan accrues interest at a periodic rate \(j\) with no payments during the next \(r\) complete periods. After one period, the balance is \(B+Bj=B(1+j)\). After a second period, interest is earned on that new balance, giving \(B(1+j)(1+j)=B(1+j)^2\). Repeating this argument period by period gives the balance after \(r\) periods.
The interest accrued over those periods is the accumulated balance less the starting balance:
This result assumes the stated periodic compounding convention and no intervening payments or other transactions. If a payment occurs before settlement, the balance must first be adjusted for that payment according to its timing. If a contract instead specifies a different day-count or accrual rule, use that rule rather than this periodic model.
Worked Example: Payoff Exactly on a Payment Date
A hypothetical loan has a principal balance of $42,600 immediately after the borrower makes the scheduled payment on the refinance date. The contract requires a prepayment penalty equal to 1.5% of that principal balance and a $125 discharge fee. There are no other amounts due or credits. Find the old loan’s payoff.
Method. Because the balance is already stated immediately after the payment on the settlement date, there is no elapsed period for which to add interest. The penalty base is explicitly the principal balance.
Calculate the penalty:
Add the penalty and fee to the balance:
The payoff is $43,364.00. The check is that the amount exceeds the principal by exactly $639 + $125 = $764. The common mistake avoided here is adding a full installment period of interest even though the balance is already dated after the settlement-date payment.
Worked Example: Accruing Interest Between Payment Dates
A hypothetical loan has a balance of $24,000 immediately after its latest payment. The contract accrues interest at a monthly rate of 1%, and the refinance settles two complete months later, before another payment is due. The lender charges a penalty equal to 2% of the principal balance, before accrued interest, and a $90 discharge fee. The borrower also has a $50 credit applicable to the old-loan payoff. Find the payoff.
Method. Accumulate the balance for two monthly periods. Then calculate the penalty on the original principal balance, as specified, and include the fee and credit.
The balance after one month is:
After the second month it is:
Thus, interest accrued since the latest payment is \(24{,}482.40-24{,}000=482.40\). The penalty is calculated on principal before accrued interest:
Assemble the settlement amount:
The payoff is $25,002.40. A check is to separate the change from the stated balance: $482.40 interest + $480 penalty + $90 fee − $50 credit = $1,002.40, which added to $24,000 gives the same total. The common mistake avoided is applying the 2% penalty to $24,482.40; the contract defines its base as principal before accrued interest.
Worked Example: Penalty Based on the Accumulated Payoff Balance
A hypothetical borrower’s balance is $40,000 immediately after a payment. The loan accrues at 1% per month, and settlement occurs three complete months later with no intervening payment. The contract imposes a penalty of 3% of the amount outstanding on the settlement date, including accrued interest. A $250 discharge fee is due, and a $100 credit applies. Calculate the payoff to the nearest cent.
Method. First find the settlement-date balance. Since the penalty base includes accrued interest, apply the 3% rate to that accumulated balance, not to the original $40,000.
The monthly accumulation factor over three months is:
Therefore, the settlement-date balance is:
The penalty, before rounding, is:
Add the fee and subtract the credit:
Rounded only at the final step to two decimal places, the payoff is $42,598.40. The calculation checks because the penalty is 3% of the accumulated balance, while the net settlement adjustments are $1,236.3612 + $250 − $100. The common mistake avoided is applying the penalty to the earlier $40,000 balance despite the explicit settlement-date penalty base.
Common Payoff Errors
The following incorrect calculation illustrates a frequent error. In the second example, suppose a borrower adds the penalty to the earlier balance and forgets to accrue interest:
This total is $482.40 too low because it omits the interest accrued over the two months. The correct calculation uses the settlement-date balance of $24,482.40 before adding the other settlement items, producing $25,002.40. Conversely, if a statement already gives the settlement-date payoff balance including accrued interest, adding that same interest again would make the result too high.
- Mixing up dates. A balance at the last payment date is not automatically the balance at refinance settlement.
- Using the wrong penalty base. A percentage of principal and a percentage of principal plus accrued interest produce different penalties.
- Double-counting. Do not add interest or a fee again if it is already included in the quoted payoff.
- Ignoring credits. Subtract a credit only when it applies to the old loan and is not already reflected in the balance.
- Confusing payoff with all refinancing funds. Include only the items that the question identifies as part of discharging the old loan.
Check Your Understanding
For each problem, identify the balance date and penalty base before assembling the payoff.
- A loan balance is $31,500 immediately after a payment made on the settlement date. A 1% penalty applies to principal, and the discharge fee is $75. There are no credits. Find the payoff. (Answer: $31,890.00)
- A $12,000 balance is stated immediately after a payment. The monthly rate is 0.75%, settlement is two complete months later, and a $40 fee applies. There is no penalty or credit. Find the payoff. (Answer: $12,220.68)
- A $50,000 balance is stated immediately after a payment. Accrue two months at 0.5% per month. The penalty is 1.5% of the original principal balance, the fee is $180, and a $25 credit applies. Find the payoff. (Answer: $51,406.25)
- A settlement-date balance of $27,840 is already stated after the scheduled payment and includes all interest through that date. The penalty is 2.25% of that balance, the discharge fee is $135, and a $60 credit applies. Find the payoff. (Answer: $28,541.40)
- A $16,000 balance is stated immediately after a payment. Accrue three months at 1% per month. The penalty is 2% of the settlement-date balance including accrued interest; the fee is $85, and the applicable credit is $40. Round the payoff to cents. (Answer: $16,859.51)