Every installment loan, lease and annuity payout rests on one factor: the level payment that exactly repays a dollar, with interest, over a set number of periods. Lenders call it a loan constant or mortgage constant; engineering-economics texts call it the capital recovery factor, written (A/P, i, n). This generator builds a table of those factors across rates and terms, per $1 or scaled to any amount you choose, such as $1,000 or $100,000.
How to generate the table
- Enter the amount borrowed — keep $1 for the classic factor table, or enter 1,000 to read payments per $1,000.
- Choose payments at the end of each period (standard loans) or in advance (leases).
- Set the range of interest rates per period and the step.
- Set the range of periods.
- Choose the decimal places.
The capital recovery factor
Payment = amount borrowed × A/P. For payments in advance, divide by (1 + i).
Worked example
A business borrows $40,000 for 5 years at 8%, repaid annually.
- Row 5, column 8%: 0.2505
- Annual payment: $40,000 × 0.250456 = $10,018.26
- Total repaid $50,091.29, so interest is about $10,091
If the same amount were a 5-year lease with payments due at the start of each year, the factor would be 0.250456 ÷ 1.08 = 0.231904, for payments of about $9,276.16.
Monthly loans: per $1,000 borrowed
Set the amount to 1,000 and use monthly rates (annual rate ÷ 12). A few common cases:
| Loan | Monthly rate | Months | Payment per $1,000 |
|---|---|---|---|
| 30-year mortgage at 6% | 0.5% | 360 | $6.00 (5.9955) |
| 15-year mortgage at 6% | 0.5% | 180 | $8.44 |
| 5-year auto loan at 7% | 0.5833% | 60 | $19.80 |
So a $250,000, 30-year mortgage at 6% costs about $1,498.88 a month, and a $30,000 auto loan at 7% for five years about $594.04.
Reading the table
- Higher rates raise payments; longer terms lower them — but with diminishing effect. At 6%, stretching a loan from 15 to 30 annual payments cuts the factor from 0.1030 to 0.0726, not in half.
- Every factor is at least the rate. Even on a very long loan you must pay at least the interest; as n grows, A/P approaches i.
- Total interest per $1 is n × factor − 1. At 6% for 30 periods that is 30 × 0.072649 − 1 = $1.18 of interest per dollar borrowed.
For exact payments with any frequency, extra payments and a full schedule, use the loan calculator or the amortization calculator. To see payments for actual loan amounts across a grid of rates and terms, try the loan payment table; the reciprocal factors are in the present value of annuity table.
Factors exclude fees, insurance and taxes and are rounded to the decimals shown. For study and planning; not financial or lending advice.
Frequently asked questions
What does a payment-per-$1 table show?
Each cell is the capital recovery factor, i ÷ [1 − (1 + i)^−n]: the level payment per period that repays $1, with interest at rate i, over n periods. Multiply it by the amount borrowed to get the payment.
How do I find a monthly mortgage payment with the table?
Use the monthly rate and the number of months. At 6% a year (0.5% a month) for 360 months, the factor is 0.0059955, or $5.9955 per $1,000. A $250,000 loan therefore costs about $1,498.88 a month in principal and interest.
What does 'payments in advance' mean?
Each payment is made at the start of its period, as with most leases and some annuity payouts. The factor is the ordinary factor divided by (1 + i), so the payment is slightly smaller.
Why is the factor for one period equal to 1 + i?
Repaying $1 in a single payment at the end of one period requires returning the dollar plus one period of interest.
How is this related to the present value of annuity table?
The factors are reciprocals. The present value of annuity factor tells you how much a $1 payment stream is worth; this table tells you how much payment a $1 lump sum supports.