Loan Amortization Payment
Level periodic payment, total interest, and payoff for a fully amortized loan.
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The engineering
This is the capital-recovery factor (A/P): it converts a present lump sum P into n equal end-of-period payments A at periodic rate i. Every fully amortized loan — mortgages, equipment financing, project debt — is this one equation, and each payment splits into interest on the outstanding balance plus principal reduction that grows as the balance falls.
Watch the compounding period: a 6.5% annual rate over 12 monthly payments uses i = 0.5417% per month, not 6.5% per period. The total-interest line is the sanity check that hurts — a 30-year loan often pays back nearly double the principal, and that number is dominated by term, not rate.
Where this math comes from
The math is compound-interest annuity theory worked out by mathematicians like Leonhard Euler and codified in actuarial and banking tables through the 1800s. The capital-recovery factor became a standard engineering-economy tool once firms needed a defensible way to compare buying versus financing capital equipment.
It reached engineers in its modern textbook form through Eugene Grant's Principles of Engineering Economy (1930) and later the widely used Blank & Tarquin Engineering Economy, where A/P, P/A, and the rest of the factor family are tabulated as the everyday language of lifecycle cost analysis.
- 1748Leonhard EulerFormalizes compound-interest and annuity series in Introductio in analysin infinitorum.
- 1930Eugene L. GrantPrinciples of Engineering Economy establishes the discrete factor notation for engineers.
- 1976Blank & TarquinEngineering Economy standardizes the A/P capital-recovery factor this card computes.
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