Why Audit an Amortization Schedule?
An amortization schedule records how each payment is divided between interest and principal and how the loan balance changes from one payment date to the next. A schedule may look plausible overall yet contain an incorrect interest charge, a balance carried forward incorrectly, or a final payment that does not actually retire the debt. Auditing means checking both the individual rows and the schedule as a whole.
The key is to use several checks, not just one. Row-by-row identities test the arithmetic within each period. Payment counts and beginning and ending balances test whether the schedule represents the stated loan. Aggregate totals test whether payments reconcile with principal and interest. These checks complement one another: a schedule can pass a total check while still having an error in an individual row.
Combining those identities gives a particularly useful row check:
This tutorial assumes interest is charged once per payment period at the stated effective rate for that period, payments are made at the ends of periods, and balances are measured immediately after payments. If a schedule uses a different payment timing or a different convention for when interest is credited, its row identity must reflect that model. Do not apply a per-period rate to a balance when the rate and payment periods do not match.
Why the Row and Total Checks Work
During period \(k\), the opening balance accumulates interest of \(iB_{k-1}\). The amount owed just before the payment is therefore \(B_{k-1}+J_k\). Subtracting the payment leaves the balance after payment. Thus \(B_k=B_{k-1}+J_k-C_k\). Rearranging shows that the payment covers the interest first in the accounting identity, with the remainder reducing principal: \(R_k=C_k-J_k\).
Summing the balance change across all \(n\) periods explains the aggregate reconciliation. In each row, the balance falls by principal repaid, so adding all row changes causes the intermediate balances to cancel:
Since \(C_k=J_k+R_k\), total payments equal total interest plus total principal repaid. If the loan starts at \(B_0\) and is fully repaid so \(B_n=0\), then:
This is a powerful check, but it is not a substitute for checking every row. An incorrect interest entry can be carried forward into later balances and payments, leaving the incorrect schedule internally consistent in aggregate.
A Practical Audit Sequence
Use a fixed sequence so that an error is not overlooked merely because the final balance appears reasonable.
Check the rate per payment period, payment timing, number of scheduled payment dates, and whether the last payment is adjusted to retire the balance.
For every row, multiply the beginning balance by the rate applying to that period. Follow the stated rounding convention.
Subtract interest from the payment to find principal repaid, then subtract that principal from the beginning balance.
Confirm that the first beginning balance is the original principal, the final balance is the stated payoff balance, and total payments equal principal repaid plus interest.
Worked Schedule Audits
Worked Example: Checking a Three-Payment Payoff
A loan of $900 accrues interest at 2% per payment period. The first two payments are $300 each, and the third payment is intended to pay off the loan. The schedule rounds interest and payments to the nearest cent each period. Audit the rows and find the final payment and total interest.
Method. Check the interest and balance in each period, rounding interest to cents, then set the final payment equal to the balance immediately before the last payment plus that period’s interest. This avoids assuming that three payments of $300 will necessarily retire the loan.
Period 1 begins with $900.00. Interest is \(900.00(0.02)=\$18.00\). The payment repays \(300.00-18.00=\$282.00\) of principal, leaving \(900.00-282.00=\$618.00\).
Period 2 begins with $618.00. Interest is \(618.00(0.02)=\$12.36\). Principal repaid is \(300.00-12.36=\$287.64\), leaving \(618.00-287.64=\$330.36\).
Period 3 begins with $330.36. The unrounded interest is \(330.36(0.02)=\$6.6072\), which rounds to $6.61. The final payment is therefore \(330.36+6.61=\$336.97\), leaving a balance of $0.00 under the stated cent-rounding convention.
Total payments are \(300.00+300.00+336.97=\$936.97\). Total interest is \(18.00+12.36+6.61=\$36.97\). The aggregate check agrees: \(\$936.97-\$900.00=\$36.97\). The schedule has three payments, begins at $900.00, ends at zero, and satisfies both the row checks and the total check.
Worked Example: Auditing a Schedule with a Regular Payment
A $2,000 loan is repaid with end-of-period payments. Interest is 1.5% per period. The first three payments are $520, and the fourth is adjusted to retire the loan. The schedule rounds each period’s interest to cents before calculating principal repaid and the new balance. Find the final payment and test the total.
Method. Recalculate each row from its opening balance, rather than relying on a displayed balance. This catches errors carried forward from an earlier row.
Period 1: interest is \(2{,}000.00(0.015)=\$30.00\). Principal repaid is \(520.00-30.00=\$490.00\), so the ending balance is \(2{,}000.00-490.00=\$1{,}510.00\).
Period 2: interest is \(1{,}510.00(0.015)=\$22.65\). Principal repaid is \(520.00-22.65=\$497.35\), leaving \(1{,}510.00-497.35=\$1{,}012.65\).
Period 3: interest before rounding is \(1{,}012.65(0.015)=\$15.18975\), or $15.19 to cents. Principal repaid is \(520.00-15.19=\$504.81\). The ending balance is \(1{,}012.65-504.81=\$507.84\).
Period 4 interest before rounding is \(507.84(0.015)=\$7.6176\), or $7.62. The payoff payment is \(507.84+7.62=\$515.46\). There are four payments: three of $520.00 and one of $515.46. Their total is \(3(520.00)+515.46=\$2{,}075.46\). Total interest is \(30.00+22.65+15.19+7.62=\$75.46\), and \(2{,}000.00+75.46=\$2{,}075.46\). The final balance is zero, and both checks agree.
Worked Example: Finding a Row Error That Totals Conceal
A $1,200 loan has a rate of 1% per period and four payments of $250 followed by a final payoff. A draft schedule lists the first three rows as follows: period 1 ends at $962.00; period 2 ends at $721.62; period 3 shows interest of $7.12, principal repaid of $242.88, and an ending balance of $478.74. It then lists period 4 interest as $4.79 and an ending balance of $233.53, followed by a final payment of $235.87. All amounts are stated to cents. Audit the draft.
Method. Recalculate each interest charge from its opening balance, and then carry the corrected balance forward. Do not accept a schedule just because its listed payments and interest happen to reconcile in total.
Period 1 checks: interest is \(1{,}200.00(0.01)=\$12.00\); principal repaid is \(250.00-12.00=\$238.00\); the ending balance is $962.00. Period 2 also checks: interest is \(962.00(0.01)=\$9.62\); principal repaid is $240.38; the ending balance is \(962.00-240.38=\$721.62\).
The period 3 interest should be \(721.62(0.01)=\$7.2162\), which rounds to $7.22, not $7.12. The correct principal repaid is \(250.00-7.22=\$242.78\), and the correct ending balance is \(721.62-242.78=\$478.84\).
Period 4 interest is \(478.84(0.01)=\$4.7884\), or $4.79. After the $250 payment, the balance is \(478.84-(250.00-4.79)=\$233.63\). The final period’s interest is \(233.63(0.01)=\$2.3363\), or $2.34, so the correct final payment is \(\$233.63+\$2.34=\$235.97\).
Correct total payments are \(4(250.00)+235.97=\$1{,}235.97\), and total interest is \(12.00+9.62+7.22+4.79+2.34=\$35.97\). The total payments also equal \(1{,}200.00+35.97=\$1{,}235.97\). The draft’s lower final payment and interest total can reconcile with each other because the period 3 error was carried forward. That aggregate agreement did not validate the incorrect row.
Common Mistakes and Rounding Traps
An audit should check both the financial model and the arithmetic. In particular, verify whether the rate is stated per payment period or per year, and whether the schedule rounds interest period by period or carries unrounded values until the end. Those conventions can produce small differences in the final balance or payment. A schedule cannot be judged against a different rounding convention without first accounting for that difference.
- Using the wrong period rate. If the payment period is monthly, do not automatically apply an annual rate as though it were a monthly effective rate. Use the rate specified for the period or convert it using the appropriate interest convention.
- Adding interest to the wrong balance. Interest for a period is based on that period’s beginning balance under the model stated here, not its ending balance.
- Confusing payment with principal repaid. The payment includes both interest and principal. Principal repaid is \(C_k-J_k\), not the full payment.
- Checking only the final balance or grand total. A carried-forward error may make the later rows and total internally consistent. Check every row against its own opening balance.
- Rounding inconsistently. Rounding an interest charge in one row but using unrounded interest in the balance calculation can create a discrepancy. Follow one convention throughout and state it.
- Counting payment dates incorrectly. Check the number of scheduled rows and whether a final adjusted payment replaces, rather than adds to, a regular payment.
For a schedule with an adjusted last payment, a small difference between a theoretical unrounded payoff and a payment stated to cents may be the result of the specified rounding rule. The relevant audit is whether the schedule’s displayed balances and payments follow that rule consistently and whether the final cash payment retires the displayed balance.
Check Your Understanding
For each problem, use the stated period rate and rounding convention. Assume end-of-period payments and round interest to cents each period unless the problem says otherwise.
- A $500 loan accrues interest at 2% per period. The first payment is $180, and the second payment is the final payoff. Find the first period’s interest and ending balance, the final payment, and total interest. (Answer: First-period interest $10.00; first ending balance $330.00; final payment $336.60; total interest $16.60.)
- A $1,000 loan accrues interest at 1% per period. The first two payments are $340, and the third is the final payoff. Find the final payment and total interest. (Answer: Final payment $340.07; total interest $20.07.)
- A schedule starts a period with a balance of $2,400. The rate is 0.5% per period and the payment is $410. Find the interest, principal repaid, and ending balance for this row. (Answer: Interest $12.00; principal repaid $398.00; ending balance $2,002.00.)
- A $600 loan accrues interest at 1% per period. The first two payments are $205, and the third is the payoff. Find the final payment, total payments, and total interest. (Answer: Final payment $202.01; total payments $612.01; total interest $12.01.)
- A $1,800 loan accrues interest at 1% per period. Its first three payments are $460, and the fourth is the payoff. A schedule reports a final payment of $465.30 and total interest of $45.30. Check these reported amounts using period-by-period cent rounding. (Answer: Final payment $465.31; total interest $45.31; each reported amount is $0.01 too low.)