Quick answer: An asset worth 500,000 with a 100,000 residual, leased at 6% for 60 months, costs 8,233.12 a month paid at month-end, or 8,192.16 paid in advance.
How it's calculated
A lease repays the asset value minus the present value of the residual: PMT = (PV − RV·(1 + r)^−n) · r ÷ (1 − (1 + r)^−n), where PV is the asset value, RV the residual value, r the annual rate ÷ 12 and n the number of months.
When each payment is due at the start of the month (in advance), the payment is the same formula divided by (1 + r), because each payment earns one month less interest. A residual of 0 gives an ordinary loan payment.
Ijara (Islamic leasing, including Ijara ending in ownership) quotes a profit rate instead of interest; the rental is worked out with the same formula. For a car lease priced with a money factor, use the car lease calculator.
Worked examples
- 500,000 value, 100,000 residual, 6%, 60 months, end of month: PMT = 8,233.12
- Same lease paid in advance: PMT = 8,233.12 ÷ 1.005 = 8,192.16
- No residual (a plain loan): PMT = 9,666.40
Frequently asked questions
What is the residual value?
The value the asset is expected to have at the end of the lease. You either pay it to own the asset (a balloon payment) or hand the asset back.
Why is the payment lower than a loan?
Because you only repay the part of the value used up during the lease; the residual is paid at the end or covered by returning the asset.
Is Ijara calculated the same way?
Yes. The Ijara rental at a fixed profit rate follows the same annuity maths. The contract terms (ownership, maintenance, insurance) differ under Shariah standards.
What is the difference between paying at month-end and in advance?
Paying in advance starts the first payment on day one, so less interest builds and the payment is slightly lower.
What happens at the end of the lease?
That depends on the contract. You may return the asset, buy it for the residual value or start a new lease.
Can I use this for equipment?
Yes. It works for cars, machines or any asset with a value, a residual, a rate and a term.