How to use the lease calculator
- Choose what to find: the lease payment, or the implied interest rate in a payment you've been quoted.
- Enter the asset value: its price or fair value at the start.
- Enter the residual value: what it will be worth, or the buyout price, at the end.
- Enter the lease term in months.
- Enter the annual interest rate, or the monthly payment if you're finding the rate.
- Choose whether payments are due at the start of each month (in advance, the usual case for leases) or at the end (in arrears).
How the lease payment is calculated
A lease is a loan on the part of the asset you use up, plus interest on the part still there at the end. The payments and the residual together must be worth the asset's value today:
Payments in advance are each made a month earlier, so each is worth a little more and the payment is lower by a factor of (1 + i). To find the rate from a payment, the calculator uses bisection: it tries a rate, checks whether the payments and residual are worth more or less than the asset, and halves the range until they match.
Worked example
The defaults are an asset worth $30,000 with a $12,000 residual after 36 months at 6%, payments in advance:
- Monthly rate: 0.06 ÷ 12 = 0.005, and (1.005)^−36 = 0.835645
- Residual in today's money: $12,000 × 0.835645 = $10,027.74
- Amount to recover through payments: $30,000 − $10,027.74 = $19,972.26
- Annuity factor: a = (1 − 0.835645) ÷ 0.005 = 32.87102, and × 1.005 = 33.03537
- Payment: $19,972.26 ÷ 33.03537 = $604.57
- 36 payments total $21,764.59, so the interest is $21,764.59 + $12,000 − $30,000 = $3,764.59
Paid in arrears instead, the payment is $19,972.26 ÷ 32.87102 = $607.59. In reverse, a quoted payment of $600 in advance implies a rate of 5.74%.
Reading the lease balance
The table shows what is still owed at each year end: $24,355.31 after year 1, $18,362.47 after year 2, and exactly the $12,000 residual at the end. At that point you either return the asset or, if the lease allows, buy it for the residual. If the asset is worth less than the residual by then, a lease where you return it puts that risk on the lessor; a lease with a guaranteed residual or a balloon puts it on you.
When to use this or the auto lease calculator
Car leases in the US quote a money factor and calculate the rent charge on the average balance, a simpler method that gives nearly the same answer. For a vehicle, use the auto lease calculator, which also handles MSRP-based residuals and sales tax. This calculator suits equipment leases, business vehicle leases and any lease where you know the value, residual and rate, or want to check the rate behind a quote. The interest rate calculator does the same for an ordinary loan with no residual.
Frequently asked questions
Why are lease payments usually made in advance?
The lessor owns the asset and hands it over on day one, so it wants the first payment at signing. That shortens the time its money is out by a month and lowers each payment a little: on the default example, $604.57 instead of $607.59.
What residual value should I use?
Use the figure in the lease agreement: the buyout price, or the value the lessor assumes at the end. For equipment, residuals depend on how fast that kind of asset loses value. A higher residual lowers the payment, because less of the asset's value has to be paid off during the lease.
Can the implied rate be negative?
Only if the payments plus the residual add up to less than the asset's value, which would mean the lessor loses money. The calculator flags that case. In practice it usually means a number was entered wrongly, such as a residual that's too low.
Does the payment include tax and fees?
No. Sales or use tax, documentation fees and insurance are extra. Add them to the payment separately, or add fees you finance to the asset value.
Related calculators
- Auto Lease Calculator — Monthly car lease payment from price, MSRP, residual value, money factor or APR, term and sales tax.
- Interest Rate Calculator — Find the annual interest rate hidden in a loan from the amount, the term and the monthly payment.
- Business Loan Calculator — Business term loan payments monthly, biweekly or weekly, with total interest, fees and the true APR.
- Payment Calculator — Monthly payment for a loan with a fixed term, or how long a fixed monthly payment takes to clear it.
Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.