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Machine tool loan and lease payment calculator
Payment = P x r / (1 - (1 + r)^-n); a 50,000 loan at 8% for 60 months is 1,013.82 a month.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Loan or lease payment
Monthly payment
per month
PMT = P x r / (1 - (1 + r)^-n) = 50,000 x 0.0066667 / (1 - (1 + 0.0066667)^-60) = 1,013.82
Total of payments 60,829.18. Total interest 10,829.18. Monthly rate r = 8 / 12 / 100 = 0.0066667.
Source: Standard amortization formula (present value of an annuity)
An estimate only. Lenders add fees, taxes and their own rounding, and lease terms such as the residual come from the lease contract. Not financial advice.
How it works
r = annual rate / 12 / 100; PMT = (P - B / (1 + r)^n) x r / (1 - (1 + r)^-n); PMT_adv = PMT / (1 + r)
| Symbol | Meaning | Unit |
|---|---|---|
| P | Amount financed | amount |
| r | Monthly interest rate, as a decimal | per month |
| n | Number of monthly payments | months |
| B | Balloon or residual value, due at the end; 0 for none | amount |
| PMT | Monthly payment, paid at the end of each month | amount per month |
| PMT_adv | Monthly payment, paid at the start of each month (payments in advance) | amount per month |
With no balloon, B = 0 and the formula reduces to PMT = P x r / (1 - (1 + r)^-n). At a 0% rate the payment is (P - B) / n. Total of payments = PMT x n, and total interest = PMT x n + B - P.
Worked example: 50,000 at 8% for 60 months
Amount financed 50,000, 8.00% a year, 60 monthly payments at the end of each month, no balloon.
- Monthly rate: r = 8 / 12 / 100 = 0.0066667.
- Discount factor: (1 + 0.0066667)^-60 = 0.67121.
- Denominator: 1 - 0.67121 = 0.32879.
- Payment: 50,000 x 0.0066667 / 0.32879 = 1,013.82 a month.
- Total of payments: 1,013.8197 x 60 = 60,829.18, figured from the unrounded payment.
- Total interest: 60,829.18 - 50,000 = 10,829.18.
Result: 1,013.82 a month, 60,829.18 in total, 10,829.18 interest.
Worked example: same loan with a 10,000 balloon
Amount financed 50,000, 8.00% a year, 60 months, balloon or residual 10,000.
- Present value of the balloon: 10,000 x 0.67121 = 6,712.10.
- Payment: (50,000 - 6,712.10) x 0.0066667 / 0.32879 = 877.72 a month.
- Payments in advance (typical lease): 877.72 / 1.0066667 = 871.91 a month.
- Total interest, end of month: 877.7224 x 60 + 10,000 - 50,000 = 52,663.35 + 10,000 - 50,000 = 12,663.35.
Result: 877.72 a month with payments at the end of each month, 871.91 with payments at the start, and 10,000 due at the end.
Notes
- Enter the amount financed after any down payment or trade-in.
- A balloon or residual lowers the monthly payment but leaves that amount due at the end of the term.
- Lease-end options, fees and taxes come from the contract. This calculator does not include them.
- Results round to 2 decimal places. A lender may round each payment differently, so the last payment can differ slightly.
FAQ
What is the payment on 50,000 at 8% over 5 years?
1,013.82 a month for 60 months, 60,829.18 in total, of which 10,829.18 is interest.
How does a balloon lower the payment?
It defers part of the principal to the end of the term: a 10,000 balloon on the same loan drops the payment to 877.72 a month, with the 10,000 due at the end.
Why is a lease payment lower than the loan payment with the same residual?
Lease payments are usually due at the start of each month, so each one is discounted by one month of interest: 871.91 against 877.72.
Does this include tax and fees?
No. Add them to the amount financed, or ask the lender how they are charged.
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