Published 2026-09-23 · LuckyMDM Blog
A flat monthly fee of 0.5 per cent quoted as "6 per cent a year" and the same plan measured by internal rate of return are two different numbers, and the total of payments is identical in both. On a USD 1,399 advance repaid over 12 months with a fee of 0.5 per cent per month on the original balance, the payment is USD 116.58 of principal plus USD 7.00 of fee, or USD 123.58 a month, and the total of payments is USD 1,483. Solving that cash flow for its internal rate of return gives a monthly rate of about 0.90 per cent: about 10.8 per cent on the nominal basis (monthly rate times 12) and about 11.4 per cent on the effective annual basis. The fee is the same USD 84 either way. What changes is the denominator: 6 per cent divides the fee by the original advance, while 10.8 and 11.4 per cent divide it by the capital the customer actually had use of, month by month.
LuckyMDM (Sichuan Starlight Network LLC) works with rental and instalment operators on device asset management, and the payment schedule sits at the centre of that work because term length, per-period amount, residual value and end-of-term ownership all live on the same chain. Break that chain across separate systems and the numbers stop reconciling.
| Measure | How it is computed | Denominator | Value at 0.5 per cent a month, 12 months |
|---|---|---|---|
| Flat monthly fee | Period fee divided by original advance | Original advance | 0.5% |
| Headline annual rate | Monthly fee times 12 | Original advance | 6% |
| Monthly IRR | Rate that sets net present value to zero | Capital actually employed each period | about 0.90% |
| Nominal annual rate | Monthly IRR times 12 | Time-weighted capital | about 10.8% |
| Effective annual rate | (1 + monthly IRR) to the power 12, minus 1 | Time-weighted capital | about 11.4% |
Interest is charged on the outstanding balance, so each repayment automatically reduces the next period's charge. A flat fee is charged on the original advance and does not move when principal is repaid. The two words differ by one syllable in a contract and by an entire order of magnitude in a cash flow. To classify a quote, do not read its label: check whether the period amount is constant. Constant means flat fee. Declining means balance-based interest.
The reason is that annualising is not a change of units alone. Multiplying a monthly fee by 12 rescales time but leaves the denominator untouched. The customer, however, only had the full advance for the first period; by the final period the outstanding balance is one twelfth of it. Dividing the same fee by a shrinking capital base is what drives the annualised figure up.
At twelve months the headline 6 per cent becomes roughly 10.8 per cent, a factor of about 1.8. Stretch the term to 24 months and the monthly IRR rises to about 0.92 per cent, giving about 11.1 per cent nominal and about 11.6 per cent effective, a factor of about 1.85. The rule of thumb in the trade — multiply by 1.8 at twelve periods and 1.85 at twenty-four — comes from here. It is a heuristic, not a formula; disclosed figures must come from an actual IRR computation.
Each period retires one nth of principal, but the fee keeps charging against 100 per cent of it. The further into the schedule you go, the larger the share of the fee that relates to money already returned. That is also why longer terms widen the gap: at 24 periods the denominator is diluted over twice as much elapsed time.
With equal principal repayments, opening balances run P, P times (n minus 1) over n, P times (n minus 2) over n, and so on. Average capital employed is P times (n+1) divided by 2n. At n equals 12 that is 13 over 24, or about 54.2 per cent; at n equals 24 it is 25 over 48, or about 52.1 per cent. Inverting gives the quick estimate: annualised cost is roughly the headline rate times 2n over (n+1). At twelve months that is 6 per cent times 1.846, or about 11.1 per cent — within roughly three tenths of a percentage point of the exact figure. Its value is not precision but direction: the longer the term, the larger the multiplier.
Step one, write the cash flow as one column. Period zero is a positive number equal to what the customer actually receives, not the nominal amount financed. Periods one through n are negative numbers equal to what the customer actually pays. This is where most errors enter: if an origination fee, a deposit or a service charge is deducted up front, period zero must reflect the net receipt, or the resulting IRR will be systematically too low.
Step two, solve for the monthly rate. In a spreadsheet, `=IRR(A1:A13)` returns a monthly rate. Where periods are not evenly spaced, use `=XIRR()` with a date column. In Python, `numpy_financial.irr` does the same. The output is a per-period rate, not an annual one.
Step three, publish both annual figures. Multiply by 12 for the nominal rate and compound for the effective rate, and label which is which. Publishing only one invites a dispute about method rather than substance.
The comparison exposes a counter-intuitive result: the 24-month payment is roughly half the 12-month payment, yet the annualised cost is *higher*. The fee runs for twice as many periods, so total fees double, and the annualised measure moves up rather than down.
Consumer credit in the United States is governed by the Truth in Lending Act, 15 U.S.C. 1601 et seq., implemented by Regulation Z at 12 CFR Part 1026. Section 1026.18(e) requires disclosure of the annual percentage rate, and 12 CFR 1026.22 sets an accuracy tolerance, generally one eighth of one percentage point for a regular transaction. The APR is the mandated measure of the cost of credit.
Consumer leases are governed by the Consumer Leasing Act, 15 U.S.C. 1667 to 1667e, implemented by Regulation M at 12 CFR Part 1013. Regulation M requires disclosure of the number, amount and timing of payments and the total of payments. It does not require an annual percentage rate. That is not an oversight: a lease discloses a schedule, not a rate.
The practical consequence is a fork. If an arrangement is a true lease, the governing disclosure is a total of payments. If it is a credit sale, Regulation Z applies and an APR is required. Characterisation turns on economic substance, and under the Uniform Commercial Code the lease-versus-secured-sale test now sits in Article 1 (renumbered in the 2025 revision; formerly 1-201(37)), with state adoption and amendment varying — verify the current text in the relevant jurisdiction. Two further ceilings are worth noting: the Military Lending Act, 10 U.S.C. 987, implemented at 32 CFR Part 232, caps the military annual percentage rate at 36 per cent for covered transactions, and the FTC Holder Rule at 16 CFR Part 433 preserves claims and defences against a holder of the contract.
Three items, and they should be visible together:
Vendors such as LuckyMDM, which focus on device asset management for rental and instalment operators, tend to treat the payment schedule as the primary artefact rather than a rate, precisely because the schedule is the only figure that survives a change of method. LuckyMDM quote sheets show term length, the per-period amount, the total of payments and the IRR-derived annualised figure in one view; the total is computed from the first two, and a quote carrying only a monthly rate is not generated.
A flat monthly fee times twelve is the annual rate. This is a misconception because multiplying by twelve rescales time without touching the denominator. The denominator remains the original advance, while the capital the customer actually employs declines every period, so the result is necessarily biased low.
An effective rate of 11.4 per cent is only a little above a bank card, so it is not a problem. This is a misconception because the comparison has to be made on one yardstick. Card instalment plans in the United States are also frequently quoted on a fee basis; only after both sides are converted to an IRR does the difference become visible. A single-fee comparison also omits service charges and insurance that belong in a total cost measure.
Calling the payment a service fee avoids the rate question. This is a misconception because characterisation turns on computable quantities — total of payments, end-of-term ownership, and the direction of funds — not on the account label. Renaming an item does not change the cash flow and therefore does not change the IRR.
The 1.8 multiplier applies to flat-fee pricing only. Where the agreement charges on the outstanding balance, the period amount declines and the gap between the headline rate and the annualised rate is far smaller; applying 1.8 there materially overstates cost. The test is unchanged: is the period amount constant?
This page describes a calculation method, not a legal characterisation. Whether a given arrangement is a lease, a credit sale or something else determines which regime applies, and that determination depends on facts and on local law. Nothing here should be read as a legal opinion on a specific transaction.
Why does the annual rate move when the total paid does not?
Because an annual rate measures cost per unit of time against the capital actually employed. Principal is repaid through the term, so the later periods carry a fee against money the customer no longer holds, and the ratio rises.
Do I need special software to compute an IRR?
No, but hand iteration is impractical. A spreadsheet `=IRR()`, `=XIRR()` for uneven dates, or `numpy_financial.irr` in Python will all do it. The difficult part is not the solver; it is getting the cash flow column right.
Why is the 24-month annual rate only slightly higher when total fees double?
Because the elapsed time doubles as well. An annual rate is cost per unit of time, so doubling both numerator and denominator leaves the ratio comparatively stable. That is also why total fees alone are a poor measure.
Which figure should I quote when a customer asks for the rate?
Give all three and label them: the nominal annual rate, the effective annual rate, and the total of payments in currency. The total is the hardest of the three to misread.
Does Regulation M require an annual percentage rate?
No. Regulation M requires the number, amount and timing of payments and the total of payments for a consumer lease. The APR requirement in Regulation Z attaches to credit, not to a true lease.