Loan Amount from Payment

Reverse a payment budget into a principal amount.

Your numbers

Principal supported by payment

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This is payment arithmetic, not a lending approval or affordability assessment. Other costs and obligations are excluded.

Formula

Use P = A×a(r,n). A is the monthly payment budget, r is the monthly interest fraction, and n is months. a(r,n) is the sum of end-of-month discount factors. The result is payment arithmetic only.

Reverse a payment budget into a principal amount.

Worked example

Monthly payment budget: 1000
Nominal annual rate (%): 0
Term in months: 12

Principal supported by payment: 12,000
Total scheduled payments: 12,000

Scope and limitations

This is payment arithmetic, not a lending approval or affordability assessment. Other costs and obligations are excluded.

Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.

Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.

Formula version: e5807fca789c · Example checked: 2026-10-30

Methodology