Multiply a money factor by 2,400 and you have the lease's annual rate: 0.0025 reads as 6.00 percent. The exact rate, the internal rate of return on the lease's cash flows, differs from that shortcut by at most 0.11 percentage point in the 63-lease grid below when the first payment is due at signing, and by up to 0.26 point when every payment falls at month end.
Neither number appears in the federal lease rule. The text and official commentary of Regulation M (12 CFR part 1013), as published on eCFR, never use the phrase "money factor," and the vehicle-lease rows the rule requires (capitalized cost, residual, depreciation, rent charge, total of base payments) are dollar amounts and counts, not rates. A money factor is a trade convention for the multiplier on the rent charge. That makes it something you can derive, and test, from the rows every vehicle-lease disclosure has to show.
Two facts carry the whole conversion. A monthly rent charge of (cost + residual) × factor equals a monthly interest rate applied to the average amount the lessor has tied up in the car, which is (cost + residual) ÷ 2; so the factor is half the monthly rate, or the annual rate divided by 24. And the exact rate is whatever monthly rate makes the lessee's cash flows (value received, payments, residual) net to zero, a calculation with no tidy formula but a short numerical solution. The gap between the two is small, systematic, and predictable from the term and the residual.
What Regulation M asks for, and what it leaves out
Regulation M implements the Consumer Leasing Act. It covers a "consumer lease," defined in 12 CFR 1013.2(e)(1) as a contract "for the use of personal property by a natural person primarily for personal, family, or household purposes, for a period exceeding four months and for a total contractual obligation not exceeding the applicable threshold amount." The threshold is indexed to the CPI-W: comment 2(e)-11 lists $71,900 for 2025 and $73,400 for 2026, and the Federal Register notice that set the 2026 figure (document 2025-22813, published December 15, 2025) is the newest Regulation M notice the Federal Register lists as of November 3, 2026. A lease whose total contractual obligation exceeds the threshold is outside the rule (comment 2(e)-9).
For a motor vehicle lease, § 1013.4(f) requires "a mathematical progression of how the scheduled periodic payment is derived," in a format substantially similar to the model forms in appendix A. It lists eleven items, in order: gross capitalized cost, capitalized cost reduction, adjusted capitalized cost, residual value, depreciation and any amortized amounts, rent charge, total of base periodic payments, number of payments, base periodic payment, an itemization of other charges that are part of the periodic payment, and the total periodic payment. A rate is not on the list. Nor is one in the statute: the Consumer Leasing Act's disclosure section, 15 U.S.C. 1667a (2023 edition on govinfo.gov), lists eleven items for every consumer lease, and none is a rate.
The rule goes further than silence when a rate does appear. Section 1013.4(s) says: "If a lessor provides a percentage rate in an advertisement or in documents evidencing the lease transaction, a notice stating that “this percentage may not measure the overall cost of financing this lease” shall accompany the rate disclosure. The lessor shall not use the term “annual percentage rate,” “annual lease rate,” or any equivalent term." Section 1013.7(b)(2) repeats the ban for advertising and adds that the rate may not be more prominent than the required disclosures. So the vocabulary a lease uses is deliberately different from a loan's. The two figures compared below are called the shortcut rate and the exact rate, and neither is an "APR" in the regulatory sense.
New Jersey's Division of Consumer Affairs, in its April 2022 "Guide to Auto Leasing," states the practical consequence in its glossary entry for the term: "State and federal law do not require lessors to disclose this key term of your contract, but it is an important factor that affects the amount of your monthly payment." The same entry gives a rule of thumb: the factor "when multiplied by the number 24 (no matter what the term of the lease), will give you a good sense of what your annual interest rate will be." Multiplying by 24 leaves the rate as a fraction (0.0025 × 24 = 0.06); multiplying by 2,400 gives the same rate in percent. The shortcut compared below is the second form of that rule.
Because the contract rows are dollar amounts, a reader can recover the factor even when no one states it. The rent charge in line (f)(6) is the total of the base payments minus the depreciation, and under the standard formula it equals the number of payments times (adjusted cost + residual) times the factor. Divide the rent charge by that product and the factor falls out. The walk-through in the next section shows the division.
The payment, one Regulation M line at a time
Let C be the adjusted capitalized cost, R the residual value, n the number of payments, and f the money factor. Section 1013.4(f)(3) describes the adjusted capitalized cost as "the amount used in calculating your base [periodic] payment." Line (f)(1) describes the gross figure it starts from as the agreed value of the vehicle "and any items you pay for over the lease term (such as service contracts, insurance, and any outstanding prior credit or lease balance)." Cash, a trade-in credit or a rebate that reduces the gross figure is the capitalized cost reduction in (f)(2). What is left is C.
The regulation defines the next three rows by subtraction. Under (f)(5), depreciation and any amortized amounts is "the difference between the adjusted capitalized cost and the residual value." Under (f)(6), the rent charge is "the amount charged in addition to the depreciation and any amortized amounts," and "This amount is the difference between the total of the base periodic payments over the lease term minus the depreciation and any amortized amounts." Under (f)(7), the total of base periodic payments is the depreciation plus the rent charge. Line (f)(9) divides that total by the number of payments.
The money factor is the missing link that turns those definitions into a payment. With the standard industry formula the rows become:
Here is one lease run through every line. The vehicle has a gross capitalized cost of $40,000, the buyer pays $3,000 in cash at signing as a capitalized cost reduction, the residual is $24,000 (60 percent of the $40,000 gross figure), the term is 36 months and the money factor is 0.0025. All of these are illustration inputs.
| Regulation M line | Label on the form | Amount |
|---|---|---|
| 1013.4(f)(1) | Gross capitalized cost (agreed value, illustrative) | $40,000.00 |
| 1013.4(f)(2) | Capitalized cost reduction (cash paid at signing) | $3,000.00 |
| 1013.4(f)(3) | Adjusted capitalized cost | $37,000.00 |
| 1013.4(f)(4) | Residual value | $24,000.00 |
| 1013.4(f)(5) | Depreciation and any amortized amounts (adjusted cost minus residual) | $13,000.00 |
| 1013.4(f)(6) | Rent charge (total of base payments minus depreciation) | $5,490.00 |
| 1013.4(f)(7) | Total of base periodic payments | $18,490.00 |
| 1013.4(f)(8) | Lease payments (number) | 36 |
| 1013.4(f)(9) | Base periodic payment (total divided by number) | $513.61 |
Monthly depreciation is $13,000 ÷ 36 = $361.11, the monthly rent is ($37,000 + $24,000) × 0.0025 = $152.50, and the sum is $513.61. The unrounded payment is $513.6111; times 36 it is $18,490.00. Rounded to the cent, 36 payments of $513.61 add to $18,489.96, four cents short. Comment 4(f)(7) in Supplement I covers exactly this: if the payment calculation is correct, the total of base periodic payments is correct for disclosure purposes "even if that amount differs from the base periodic payment disclosed under § 1013.4(f)(9) multiplied by the number of lease payments disclosed under § 1013.4(f)(8), when the difference is due to rounding."
The auto lease calculator runs this same progression on your own figures. It takes depreciation as (adjusted cost minus residual) divided by the term and rent as (adjusted cost plus residual) times the factor, treats the down payment as a capitalized cost reduction, accepts either a factor or a rate (a rate is divided by 2,400 to get the factor), and adds sales tax as a percentage of the base payment, with a default of 13 percent. With the tax set to 0, the table's inputs ($40,000 price, $3,000 down, $24,000 residual, 36 months, factor 0.0025) return $513.61.
Now run the recovery described earlier on the disclosed rent charge: $5,490 ÷ (36 × ($37,000 + $24,000)) = $5,490 ÷ $2,196,000 = 0.0025. The factor is recoverable from the form even though no row names it.
The other disclosure lines add cash around the payment schedule:
| Regulation M line | Item | Amount |
|---|---|---|
| 1013.4(b) | Amount due at signing: cap cost reduction plus first payment | $3,513.61 |
| 1013.4(c) | Total of the periodic payments | $18,490.00 |
| 1013.4(d) | Other charges: assumed disposition fee at lease end | $395.00 |
| 1013.4(e) | Total of payments: signing amount, plus remaining periodic payments, plus other charges | $21,885.00 |
The amount due at signing here is the $3,000 reduction plus the first monthly payment, since § 1013.4(b) lists "advance monthly or other periodic payment" among the components of the signing amount. The $395 disposition fee is an assumed input, not a market figure. The total of payments in (e) is the signing amount, plus the periodic payments not already collected at signing, plus other charges: $3,513.61 + $17,976.39 + $395.00 = $21,885.00.
A published example, recomputed
A payment formula should reproduce numbers someone else printed before it is trusted with new ones. Craig G. White's "Lease or Purchase? A Spreadsheet Analysis" (The CPA Journal, July 2001) works one case in full: a 48-month lease of a car with a capitalized cost of $25,000 and a residual of $13,750, at an 8.5 percent APR, which the article writes as a money factor of .003542. It states the factor's origin plainly: "The money factor is the annual percentage rate (APR) divided by 24." The article's arithmetic and the recomputed values:
| Item | As printed | Recomputed |
|---|---|---|
| Money factor (APR 8.5% divided by 24) | .003542 | 0.0035417 |
| Monthly depreciation, (25,000 − 13,750) / 48 | $235 | $234.375 |
| Monthly rent charge, (25,000 + 13,750) × .003542 | $137 | $137.252 |
| Monthly payment | about $372 | $371.627 |
| Present value of the $13,750 residual at 8.5%, four annual periods | $9,922 | $9,921.65 |
| Amount financed in present-value terms | $15,078 | $15,078 |
| Payment on $15,078 at 8.5%/12 over 48 months | $372 | $371.647 |
| Payment to buy the car: $25,000 at 8.5%/12 over 48 months | $616 | $616.208 |
| Purchase cost net of a $13,750 sale: 616 × 48 − 13,750 | $15,818 | $15,818 |
The formula reproduces the example to the article's own rounding, which is as close as a printed whole-dollar example allows. The monthly rent comes out at $137.25 against the printed $137, and the payment at $371.63 against the printed "approximately $372." The residual's present value, the $15,078 of value used, the $372 payment on that value and the $616 purchase payment all match to the dollar. One printed line is high: the monthly depreciation, $11,250 ÷ 48, is $234.375, which rounds to $234, and the article prints $235. The printed $235 plus $137 gives the $372 total; the exact sum is $371.63, which rounds to the same $372. The exact check of the formula is the Regulation M walk-through above, where every row foots to the cent. One further figure in the article, a nominal lease cost of $17,389, does not follow from the others (the $372 payment times 48 months is $17,856), and nothing else here relies on it.
The article's present-value step compounds the residual in four annual periods at 8.5 percent. Compounding monthly (8.5 percent ÷ 12, 48 months) gives $9,798.58 instead of $9,921.65, so the article's second method is an approximation that happens to land on the same $372 payment to the dollar.
The example also supplies a first test of the shortcut. The lease is labeled 8.5 percent, and the factor times 2,400 gives 8.50 percent. The internal rate of return on its cash flows is 8.47 percent if the first payment is made at signing and 8.32 percent if all 48 payments fall at month end. The gap in the second case, 0.18 point, falls inside the 0.26-point worst case of the month-end calculation across the 63-lease grid below, where the signing-day worst case is 0.11 point. Which timing convention applies decides which of these exact figures is the right one to hold the shortcut against, and the section on timing returns to that.
Where the 24 comes from
Regulation M never explains the factor, and the two published sources quoted above (the New Jersey guide and the CPA Journal article) state the divisor without a derivation. Here is the short algebra.
Let r be the annual rate and i = r ÷ 12 the monthly rate. Picture the lessor's investment in the car falling in a straight line from C at signing to R at the end of the term. The balance at the end of month k is
and the interest for month k, charged on the average of the opening and closing balances, is i × (opening balance + closing balance) ÷ 2. Those n monthly averages lie evenly along a straight line from C to R, so their mean is the midpoint of the line, (C + R) ÷ 2, exactly. Each month's rent therefore averages
Setting that equal to the rent in the payment formula, (C + R) × f, gives
The checks are quick. A 6 percent rate divided by 24 is 0.0025. A factor of 0.0030 is 7.2 percent, and 0.0020 is 4.8 percent. A numeric check of the averaging step for the $40,000, $24,000, 36-month lease: the average of the 36 closing balances alone is $31,777.78, the average of the 36 opening balances is $32,222.22, and the average of the two-point averages is $32,000.00, which is (40,000 + 24,000) ÷ 2. At 0.5 percent a month, $32,000 of average balance carries $160.00 of rent, and (40,000 + 24,000) × 0.0025 is $160.00.
One consequence is easy to miss. The rent is charged on (C + R) ÷ 2, not on the average depreciated value, so the residual bears interest for the entire term. Of the 36-month lease's $5,760 total rent at 0.0025 (36 × $160), $4,320 is 6 percent on the $24,000 residual for 36 months (36 × 0.005 × $24,000) and $1,440 is 6 percent on half the $16,000 of depreciation (36 × 0.005 × $8,000). The New Jersey guide says it in one sentence: "Remember, you are also paying finance charges on the residual."
The straight-line balance is a bookkeeping device. A lessor's actual balance, with level payments, declines along a curve, and the shortcut is not exact for that reason. The next sections measure how far off it is.
The exact rate is an internal rate of return
The accurate version of "what annual rate does this lease charge" is the same idea Regulation Z uses for loans. Section 1026.22(a)(1) of that regulation says: "The annual percentage rate is a measure of the cost of credit, expressed as a yearly rate, that relates the amount and timing of value received by the consumer to the amount and timing of payments made." For a lease, the value received is the vehicle's adjusted capitalized cost at signing; the payments are the n installments; and the lessor gets the residual back at the end, from a buyout or from selling the car. Find the monthly rate i at which the present value of those payments plus the residual equals C, and multiply by 12.
With v = 1 ÷ (1 + i), the first payment due at signing gives
and payments at the end of each month give
Neither equation can be solved for i in closed form. A spreadsheet's rate function or a few dozen bisection steps finds it. Bisection on the 36-month lease above gives 6.0273 percent a year if the first payment is collected at signing and 5.9276 percent if all payments fall at month end, against 6.0000 percent from the shortcut. To confirm the solution, roll the lessor's balance forward at the solved rate: start at $37,000, subtract a payment, add a month's interest, and repeat 36 times. The balance after the last month is $24,000.0000, the residual.
Three modelling choices sit behind these numbers.
- The residual is treated as money recovered. In a closed-end lease the lessee is not responsible for it; Supplement I, comment 2(d)-1, describes such a lease as one where "the lessee is not responsible for the residual value of the leased property at the end of the lease term." The lessor bears the difference if the car sells for less, so the rate here is the rate the contract is priced at, not a guarantee of what the lessor earns.
- C is the adjusted capitalized cost. The cash reduction at signing is already out of it, which keeps the cash flow at time zero to a single number.
- The first payment's timing is a contract fact. Section 1013.4(b) names the advance periodic payment as a possible component of the signing amount. The disclosure shows whether it is collected up front.
The annual figure is 12 times the monthly rate, a nominal rate and the same convention as a loan's stated rate. A compounded annual yield would be higher (6.00 percent nominal compounds to 1.005^12 − 1 = 6.17 percent) and is not used in any table here.
How close the shortcut is: a grid of 63 leases
The grid uses a $40,000 vehicle (the residual percentage is taken of that figure), terms of 24, 36 and 48 months, residuals of 50, 60 and 70 percent, and seven money factors from 0.0010 to 0.0040. Payments first:
| Term (months) | Money factor | Shortcut × 2,400 | Payment, 50% residual ($20,000) | Payment, 60% residual ($24,000) | Payment, 70% residual ($28,000) |
|---|---|---|---|---|---|
| 24 | 0.0010 | 2.40% | $893.33 | $730.67 | $568.00 |
| 24 | 0.0015 | 3.60% | $923.33 | $762.67 | $602.00 |
| 24 | 0.0020 | 4.80% | $953.33 | $794.67 | $636.00 |
| 24 | 0.0025 | 6.00% | $983.33 | $826.67 | $670.00 |
| 24 | 0.0030 | 7.20% | $1,013.33 | $858.67 | $704.00 |
| 24 | 0.0035 | 8.40% | $1,043.33 | $890.67 | $738.00 |
| 24 | 0.0040 | 9.60% | $1,073.33 | $922.67 | $772.00 |
| 36 | 0.0010 | 2.40% | $615.56 | $508.44 | $401.33 |
| 36 | 0.0015 | 3.60% | $645.56 | $540.44 | $435.33 |
| 36 | 0.0020 | 4.80% | $675.56 | $572.44 | $469.33 |
| 36 | 0.0025 | 6.00% | $705.56 | $604.44 | $503.33 |
| 36 | 0.0030 | 7.20% | $735.56 | $636.44 | $537.33 |
| 36 | 0.0035 | 8.40% | $765.56 | $668.44 | $571.33 |
| 36 | 0.0040 | 9.60% | $795.56 | $700.44 | $605.33 |
| 48 | 0.0010 | 2.40% | $476.67 | $397.33 | $318.00 |
| 48 | 0.0015 | 3.60% | $506.67 | $429.33 | $352.00 |
| 48 | 0.0020 | 4.80% | $536.67 | $461.33 | $386.00 |
| 48 | 0.0025 | 6.00% | $566.67 | $493.33 | $420.00 |
| 48 | 0.0030 | 7.20% | $596.67 | $525.33 | $454.00 |
| 48 | 0.0035 | 8.40% | $626.67 | $557.33 | $488.00 |
| 48 | 0.0040 | 9.60% | $656.67 | $589.33 | $522.00 |
At a 60 percent residual, each 0.0005 step in the factor adds $32.00 a month, which is 0.0005 × ($40,000 + $24,000). The step is the same at 24, 36 and 48 months, because the monthly rent depends on the cost plus the residual and the factor, not on the term. A 10-point higher residual lowers the 36-month payment at 0.0025 by $101.11 (from $604.44 to $503.33), which is $4,000 × (1 ÷ 36 − 0.0025): less depreciation to pay down, partly offset by rent on the larger residual.
Now the exact rate for each of those 63 leases, with the first payment due at signing:
| Term (months) | Money factor | Shortcut × 2,400 | Exact, 50% residual | Exact, 60% residual | Exact, 70% residual | Shortcut minus exact (60%), points |
|---|---|---|---|---|---|---|
| 24 | 0.0010 | 2.40% | 2.432% | 2.425% | 2.419% | −0.025 |
| 24 | 0.0015 | 3.60% | 3.647% | 3.638% | 3.630% | −0.038 |
| 24 | 0.0020 | 4.80% | 4.861% | 4.850% | 4.841% | −0.050 |
| 24 | 0.0025 | 6.00% | 6.074% | 6.063% | 6.053% | −0.063 |
| 24 | 0.0030 | 7.20% | 7.286% | 7.276% | 7.266% | −0.076 |
| 24 | 0.0035 | 8.40% | 8.498% | 8.488% | 8.480% | −0.088 |
| 24 | 0.0040 | 9.60% | 9.708% | 9.701% | 9.694% | −0.101 |
| 36 | 0.0010 | 2.40% | 2.417% | 2.414% | 2.412% | −0.014 |
| 36 | 0.0015 | 3.60% | 3.623% | 3.620% | 3.617% | −0.020 |
| 36 | 0.0020 | 4.80% | 4.825% | 4.824% | 4.822% | −0.024 |
| 36 | 0.0025 | 6.00% | 6.026% | 6.027% | 6.028% | −0.027 |
| 36 | 0.0030 | 7.20% | 7.224% | 7.229% | 7.233% | −0.029 |
| 36 | 0.0035 | 8.40% | 8.419% | 8.429% | 8.438% | −0.029 |
| 36 | 0.0040 | 9.60% | 9.613% | 9.629% | 9.643% | −0.029 |
| 48 | 0.0010 | 2.40% | 2.409% | 2.408% | 2.407% | −0.008 |
| 48 | 0.0015 | 3.60% | 3.607% | 3.608% | 3.609% | −0.008 |
| 48 | 0.0020 | 4.80% | 4.801% | 4.806% | 4.810% | −0.006 |
| 48 | 0.0025 | 6.00% | 5.992% | 6.001% | 6.010% | −0.001 |
| 48 | 0.0030 | 7.20% | 7.179% | 7.195% | 7.209% | +0.005 |
| 48 | 0.0035 | 8.40% | 8.362% | 8.386% | 8.407% | +0.014 |
| 48 | 0.0040 | 9.60% | 9.542% | 9.575% | 9.604% | +0.025 |
The 24-month leases have an exact rate 0.019 to 0.108 point above the shortcut. At 36 months, every one of the 21 leases is 0.012 to 0.043 point above it. At 48 months the sign changes: the shortcut ranges from 0.010 point below the exact rate to 0.058 point above it, and 14 of the 21 leases have an exact rate above the shortcut. The residual hardly matters at 36 months and 0.0025: the exact rate is 6.026 percent at a 50 percent residual and 6.028 percent at 70. The largest gap in the grid is 0.108 point (24 months, 50 percent residual, factor 0.0040), and in dollar terms it is small: 0.108 ÷ 2,400 × ($40,000 + $20,000) is $2.71 a month on a $1,073.33 payment. The 36-month lease at 0.0025 and a 60 percent residual has a gap of 0.027 point, or $0.71 a month.
For scale only: Regulation Z, 12 CFR 1026.22(a)(2), allows a loan's disclosed APR to be off by "1/8 of 1 percentage point" (0.125 point) in the regular case. That tolerance governs credit disclosures, not leases, but every signing-day gap in this grid is inside that margin.
Two timing conventions, two signs
The same payment implies a higher rate when it is paid earlier. Collect each installment a month sooner and the lessee repays the same dollars earlier, so the rate that balances the cash flows rises. Nine leases at a 0.0025 factor show both versions:
| Term (months) | Residual | Payment | Exact, first payment at signing | Shortcut minus exact | Exact, payments at month end | Shortcut minus exact |
|---|---|---|---|---|---|---|
| 24 | 50% | $983.33 | 6.074% | −0.074 | 5.880% | +0.120 |
| 24 | 60% | $826.67 | 6.063% | −0.063 | 5.909% | +0.091 |
| 24 | 70% | $670.00 | 6.053% | −0.053 | 5.936% | +0.064 |
| 36 | 50% | $705.56 | 6.026% | −0.026 | 5.888% | +0.112 |
| 36 | 60% | $604.44 | 6.027% | −0.027 | 5.915% | +0.085 |
| 36 | 70% | $503.33 | 6.028% | −0.028 | 5.940% | +0.060 |
| 48 | 50% | $566.67 | 5.992% | +0.008 | 5.883% | +0.117 |
| 48 | 60% | $493.33 | 6.001% | −0.001 | 5.911% | +0.089 |
| 48 | 70% | $420.00 | 6.010% | −0.010 | 5.937% | +0.063 |
With month-end payments the shortcut runs high in every one of the nine rows, by 0.060 to 0.120 point, and in all 63 grid leases it exceeds the month-end exact rate, by 0.015 to 0.258 point. With signing-day payments the shortcut runs low in eight of nine rows here. In 56 of the 63 grid leases the shortcut falls between the two exact figures. In the other 7, both exact rates sit below it: all seven are 48-month leases, at 50 or 60 percent residuals and the higher factors, where the signing-day exact rate drops under the shortcut.
The shortcut itself does not say when the first payment is due. The disclosure does: the amount due at signing, itemized under § 1013.4(b), either includes a periodic payment or does not. Where a lease collects the first payment up front, the signing-day column is the one to hold against the shortcut.
The affordability guide's lease example matches a month-end calculation. Its $35,000 car, 48 months, $17,500 residual and 8.99 percent rate give a payment of $566.51, which is the end-of-month payment on a loan with a $17,500 balloon ($566.5093 unrounded). The money factor that reproduces $566.51 is 0.003846, and 0.003846 × 2,400 is 9.23 percent, 0.24 point above the 8.99 percent used to build it. Conversely, a lessor who priced that lease at the shortcut factor, 8.99 ÷ 2,400 = 0.003746, would charge $561.24, $5.27 less. The how much car can you afford guide, written for Canadian buyers and adding a hypothetical 13 percent tax to each lease payment, states its lease inputs and tax assumptions; the difference here is only which convention converts a rate into a payment.
A first-order formula for the gap
The gap is not random. For month-end payments, expand the annuity factor in powers of the monthly rate i. With ρ = R ÷ C, the payment per dollar of cost is
The money-factor payment per dollar is (1 − ρ) ÷ n + (1 + ρ) f. The depreciation term (1 − ρ) ÷ n matches, and equating the next terms yields the factor that reproduces the exact payment:
Payments at the start of each month are the month-end payments discounted by one month, which changes the sign of the correction:
The relative gap is e = (1 − ρ) ÷ (n(1 + ρ)), which equals the monthly depreciation divided by cost plus residual, or (C − R) ÷ (n (C + R)). It shrinks with a longer term and with a higher residual, since less of the cost is repaid each month relative to the cost plus the residual. The table tests the formula against a numerical solution at a 2.4 percent rate (factor 0.0001), where second-order terms are small:
| Term (months) | Residual | Predicted gap, (1 − ρ) / (n (1 + ρ)) | Computed: shortcut below exact (first payment at signing) | Computed: shortcut above exact (month-end payments) |
|---|---|---|---|---|
| 24 | 50% | 1.39% | 1.38% | 1.42% |
| 36 | 60% | 0.69% | 0.68% | 0.72% |
| 36 | 30% | 1.50% | 1.45% | 1.56% |
| 48 | 70% | 0.37% | 0.36% | 0.40% |
| 60 | 50% | 0.56% | 0.51% | 0.62% |
| 12 | 60% | 2.08% | 2.09% | 2.09% |
The predicted and computed relative gaps (the computed ones divide the shortcut-minus-exact difference by the exact rate) agree to within about 0.06 percentage point in every row, so the formula sizes the error for any lease in this family. For a 36-month lease at a 60 percent residual, e = 0.4 ÷ (36 × 1.6) = 0.69 percent. On a 6 percent shortcut that is 0.04 point, the right order against the 0.027 point computed in the grid; the table above sits at 2.4 percent, and at higher rates second-order terms pull the result around, which is why the signing-day gap changes sign on the 48-month leases at higher factors.
When the gap grows
Within 24 to 48 months and mid-range residuals the shortcut looks harmless. Move to the edges and it is not:
| Term (months) | Residual | Money factor | Payment | Shortcut | Exact, first payment at signing | Gap | Exact, month end | Gap |
|---|---|---|---|---|---|---|---|---|
| 12 | 60% | 0.0025 | $1,493.33 | 6.00% | 6.143% | −0.143 | 5.864% | +0.136 |
| 24 | 40% | 0.0025 | $1,140.00 | 6.00% | 6.086% | −0.086 | 5.847% | +0.153 |
| 24 | 50% | 0.0080 | $1,313.33 | 19.20% | 19.367% | −0.167 | 18.564% | +0.636 |
| 36 | 40% | 0.0080 | $1,114.67 | 19.20% | 18.969% | +0.231 | 18.276% | +0.924 |
| 48 | 50% | 0.0080 | $896.67 | 19.20% | 18.856% | +0.344 | 18.338% | +0.862 |
| 60 | 30% | 0.0025 | $596.67 | 6.00% | 5.926% | +0.074 | 5.798% | +0.202 |
| 60 | 30% | 0.0080 | $882.67 | 19.20% | 18.200% | +1.000 | 17.669% | +1.531 |
| 72 | 30% | 0.0080 | $804.89 | 19.20% | 17.934% | +1.266 | 17.467% | +1.733 |
A 12-month lease with a 60 percent residual is off by about 0.14 point at 6 percent in either convention, because e = 0.4 ÷ (12 × 1.6) is 2.1 percent of the rate. A 60-month lease with a 30 percent residual at a 0.0080 factor, 19.20 percent by the shortcut, has an exact rate of 18.20 percent with the first payment at signing and 17.67 percent at month end: a gap of 1.0 and 1.5 points. The 72-month row is the extreme at 1.27 and 1.73 points. These are deliberately stretched inputs to show the direction of the error, not a claim about what leases are offered. The first-order gap e grows as the term shortens or the residual falls, and the second-order terms that were negligible at 2.4 percent grow with the rate times the term.
Rounding in the quote matters as much as the formula. A factor shown to four decimals, 0.0025, may be 0.00249 or 0.00251. Each 0.00001 is 0.024 point of rate and, on the 36-month example, $0.64 a month or $23.04 over the term. A 0.0001 step is 0.24 point and $6.40 a month, $230.40 over 36 months.
What neither rate includes: fees at signing
Both rates measure the financing built into the monthly payment. A fee that the lessee pays separately changes what the lease costs without touching the factor. The table uses illustrative fee amounts (not a claim about market fees) on the 36-month lease at 0.0025 and a 60 percent residual:
| Illustrative fee | Monthly payment | Exact rate to the lessee | Basis |
|---|---|---|---|
| None | $604.44 | 6.027% | none |
| $595.00 paid at signing, outside the financed amount | $604.44 | 6.710% | rate on $39,405 net |
| $595.00 added to the capitalized cost | $622.46 | 6.703% | rate on $40,000 of value received |
| $995.00 paid at signing, outside the financed amount | $604.44 | 7.177% | rate on $39,005 net |
| $995.00 added to the capitalized cost | $634.57 | 7.158% | rate on $40,000 of value received |
| $1,495.00 paid at signing, outside the financed amount | $604.44 | 7.769% | rate on $38,505 net |
| $1,495.00 added to the capitalized cost | $649.71 | 7.726% | rate on $40,000 of value received |
A $995 fee paid at signing and left out of the financed amount lifts the lessee's exact rate from 6.027 percent to 7.177 percent with the payment unchanged at $604.44. If the same fee is capitalized instead, the payment rises to $634.57 and the lease's rate on its own adjusted cost stays at 6.027 percent, but measured against the $40,000 of value the lessee receives, the rate is 7.158 percent. Supplement I, comment 4(f)(1)-1, allows capitalized taxes and fees for "title, licenses, and registration" to sit in the agreed value of the vehicle, so charges that are capitalized sit inside C and carry the factor's rent with them. This is the practical content of the notice in § 1013.4(s) that a lease's percentage "may not measure the overall cost of financing this lease": the factor prices the money, and the fees are priced elsewhere on the form.
The same car as a loan
The $40,000 vehicle, 36 months, a 60 percent residual, and a loan at the shortcut rate of each factor:
| Money factor | Rate (× 2,400) | Lease payment | Loan payment, 36 months, same rate | Loan minus lease | Loan with a $24,000 balloon at the exact rate | Lease rent charge, 36 months | Loan interest, 36 months |
|---|---|---|---|---|---|---|---|
| 0.0010 | 2.40% | $508.44 | $1,152.70 | $644.26 | $508.44 | $2,304.00 | $1,497.25 |
| 0.0020 | 4.80% | $572.44 | $1,195.25 | $622.80 | $572.44 | $4,608.00 | $3,028.91 |
| 0.0025 | 6.00% | $604.44 | $1,216.88 | $612.43 | $604.44 | $5,760.00 | $3,807.59 |
| 0.0030 | 7.20% | $636.44 | $1,238.74 | $602.30 | $636.44 | $6,912.00 | $4,594.82 |
| 0.0040 | 9.60% | $700.44 | $1,283.19 | $582.74 | $700.44 | $9,216.00 | $6,194.79 |
At these inputs the loan payment is about twice the lease payment, because the loan retires the whole $40,000 while the lease retires only the $16,000 of depreciation. The sixth column checks the identity behind the exact rate: a loan on the same $40,000 with a $24,000 balloon due at month 36, at the lease's exact (signing-day) rate with payments at the start of each month, costs exactly the lease payment. A closed-end lease is a balloon loan whose balloon the borrower is allowed to walk away from.
The gap between an ordinary loan and the balloon loan is a clean quantity. At 6.00 percent with month-end payments the ordinary loan is $1,216.88 and the balloon loan is $606.75. The $610.13 difference is the monthly sinking payment that retires $24,000 in 36 months at 0.5 percent a month: 24,000 × 0.005 ÷ (1.005^36 − 1). The loan payment is the balloon loan plus the cost of paying off the residual slice.
The last two columns of the table need care. At a 0.0025 factor the lease charges $5,760 of rent and the loan charges $3,807.59 of interest at the same 6.00 percent. That is not a hidden higher lease rate. The loan's interest falls as the balance falls, to nothing at month 36. The lease's balance never drops below the residual, so $4,320 of the $5,760 is interest on that residual slice, as shown above. The two totals are different quantities. In present value at 0.5 percent a month, the loan's net cost is its $40,000 less the present value of a car still worth $24,000 at month 36 ($20,055.48), which is $19,944.52. A balloon loan with the same $24,000 balloon has the same present cost, because its payments are worth C minus the present value of the balloon. Equal rates give an equal present cost if the car is in fact worth the residual at the end. What differs is who holds the risk of its worth and when the cash moves.
A comparison of simple totals misleads for the same reason. The loan's payments total $43,807.59; less a $24,000 car that is $19,807.59, against $21,760.00 of lease payments. The $1,952.41 difference is essentially a timing effect: the loan borrower pays about $612 more every month and gets the $24,000 back at the end, and money paid earlier is worth more than money received later. It is not a pricing difference at equal rates. Nothing here ranks one structure above the other; the arithmetic only shows that the same rate produces two very different payment shapes.
Residual changes the picture predictably:
| Residual | Lease payment | Loan payment at 6.00% | Loan minus lease | Interest the lease charges on the residual over 36 months |
|---|---|---|---|---|
| 40% ($16,000) | $806.67 | $1,216.88 | $410.21 | $2,880.00 |
| 50% ($20,000) | $705.56 | $1,216.88 | $511.32 | $3,600.00 |
| 60% ($24,000) | $604.44 | $1,216.88 | $612.43 | $4,320.00 |
| 70% ($28,000) | $503.33 | $1,216.88 | $713.54 | $5,040.00 |
The lease payment moves by $101.11 for every 10 points of residual, and the loan payment does not move at all. The "loan minus lease" gap widens by that amount. The auto loan calculator hub covers the loan side of the comparison, and the APR calculator handles a loan's own rate.
Reading a quoted payment backwards
A dealer's quote is often a payment, not a factor. If the quote is a base payment (line (f)(9), before sales tax and before any other charge folded into the periodic payment, which (f)(11) adds), the factor follows by rearranging the payment formula:
For the $40,000 vehicle with a $24,000 residual and 36 months, five hypothetical quotes:
| Quoted payment | Implied money factor | Shortcut × 2,400 | Exact, first payment at signing | Exact, month end |
|---|---|---|---|---|
| $500.00 | 0.000868 | 2.08% | 2.096% | 2.064% |
| $560.00 | 0.001806 | 4.33% | 4.356% | 4.281% |
| $620.00 | 0.002743 | 6.58% | 6.611% | 6.486% |
| $700.00 | 0.003993 | 9.58% | 9.612% | 9.408% |
| $760.00 | 0.004931 | 11.83% | 11.858% | 11.586% |
A $560 base payment implies a factor of 0.001806, a shortcut rate of 4.33 percent and an exact rate of 4.36 percent with the first payment at signing. The method assumes the quote uses the standard formula, with C meaning the adjusted capitalized cost after any reduction. A payment that includes tax or a recurring fee gives a factor that is too high. The formula is also a convention rather than a rule: if a lessor builds anything other than interest into the rent charge, the recovered factor will not match the one it states. A difference between the two is a prompt to ask which items are in the payment, nothing more.
Rolled-in balances and the factor's leverage
Line (f)(1) lets "any outstanding prior credit or lease balance" ride in the gross capitalized cost, so negative equity from a trade-in can be capitalized. Each dollar added to C raises the payment by 1 ÷ n + f, and the total repaid by 1 + n × f. For the 36-month, 0.0025 lease, $3,000 of rolled-in balance adds $90.83 a month (from $604.44 to $695.28) and $3,270 over the term, 9 percent more than the balance itself. The rolling negative equity guide works the loan version, including how many months a rolled-in shortfall keeps a buyer upside down.
Set the size of the errors against the size of the levers. The shortcut's worst error in the grid is worth $2.71 a month. A single 0.0005 step in the factor is worth $32.00 a month, or $1,152.00 over 36 months on the $40,000 example, nearly twelve times as much. The conversion error is a second-order matter; the first-order ones are the factor itself, the residual, the capitalized cost and the fees.
Interest-deduction rules do not reach a lease either. The final regulations behind the new car loan interest deduction exclude lease financing, as the car loan interest deduction guide sets out, so the rent charge is not deductible under that provision.
What a rate cannot tell you about a quote
The tables stop at the base payment. Sales or use tax on a lease follows state rules, and the figures above exclude it. Mileage allowances, excess-use charges and end-of-lease fees sit outside the payment too. The rule requires notices substantially similar to two warnings about those costs. Section 1013.4(h)(3) gives: "Excessive Wear and Use. You may be charged for excessive wear based on our standards for normal use." Section 1013.4(g)(2) gives: "Early Termination. You may have to pay a substantial charge if you end this lease early. The charge may be up to several thousand dollars. The actual charge will depend on when the lease is terminated. The earlier you end the lease, the greater this charge is likely to be." In a closed-end lease the lessee is not responsible for the residual, but those charges sit outside the payment tables. The residual itself is a number the lessor sets in the contract and uses in the payment calculation, per line (f)(4).
The calculations are arithmetic on stated inputs and published rules, not a recommendation to lease, buy, or accept any particular factor. The residual percentages, fees and money factors used above are illustrations chosen to show the mechanics.
To run a quote, enter the cost, down payment, residual, term and factor in the auto lease calculator, with tax set to 0 to see the base payment on line (f)(9); set the same cost and term in the auto loan calculator to see the loan side. Then recompute the exact rate from the disclosure's own rows, using the formulas above, and compare it with the 2,400 shortcut. The difference between the two is the part of the lease rate the shortcut hides. More guides on cars and borrowing are listed on the guides hub.
Sources
- Consumer Financial Protection Bureau, Regulation M, 12 CFR part 1013: § 1013.2(e)(1), § 1013.4(b), (c), (d), (e), (f)(1) to (f)(11), (g)(2) and (s), § 1013.7(b)(2), Supplement I comments 2(d)-1, 2(e)-11, 4(f)(1)-1 and 4(f)(7)-1, on the eCFR API (https://www.ecfr.gov/api/versioner/v1/full/2026-10-30/title-12.xml?part=1013), current text up to date as of October 30, 2026; the section's last substantive version dates from 2017, and the only later entry (2023) is marked non-substantive in the eCFR version history. The Appendix A model forms are not part of the searchable text on eCFR, so the check that the phrase "money factor" is absent covers the regulation text and Supplement I. Checked November 3, 2026.
- Federal Register, "Consumer Leasing (Regulation M)," document 2025-22813, published December 15, 2025 (annual threshold adjustment to $73,400 effective January 1, 2026), via the Federal Register API; no later Regulation M notice listed. Checked November 3, 2026.
- 15 U.S.C. 1667a, Consumer lease disclosures, United States Code 2023 edition on govinfo.gov (https://www.govinfo.gov/content/pkg/USCODE-2023-title15/html/USCODE-2023-title15-chap41-subchapI.htm). Checked November 3, 2026.
- Consumer Financial Protection Bureau, Regulation Z, 12 CFR 1026.22(a)(1) and (a)(2), eCFR API, current text up to date as of October 30, 2026. Checked November 3, 2026.
- State of New Jersey, Office of the Attorney General, Division of Consumer Affairs, "Don't Be Taken for a Ride: Guide to Auto Leasing," April 2022 (https://www.njconsumeraffairs.gov/News/Consumer%20Briefs/guide-to-auto-leasing.pdf), glossary entry "Money Factor" and the sections "Now, let's look at leasing" and "Learn how to calculate the interest rate or money factor." Checked November 3, 2026.
- Craig G. White, "Lease or Purchase? A Spreadsheet Analysis," The CPA Journal, July 2001 (http://archives.cpajournal.com/2001/0700/dept/d076601.htm), Example 1. Checked November 3, 2026.
- Payments, exact rates, gaps, fee, loan and quote tables: calculated here from the formulas shown above, with the cost, residual, term, factor and fee values stated as illustration inputs. Exact rates are solved by bisection and confirmed by rolling the lessor's balance forward to the residual.
- Scope note: state vehicle-lease tax rules are outside this guide.