How Loan Calculators Work
By Calculator Atlas editorial (draft)Publication date pending6 min read
Learn how monthly payments, interest and total cost are estimated for a fixed-rate loan.
The idea behind a loan payment
A fixed-rate loan is repaid in equal monthly payments. Each payment covers the interest accrued that month and reduces the remaining principal.
The payment formula
With principal P, monthly rate r and n monthly payments, the payment M is:
- M = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
Total interest and total cost
Total paid is M × n. Total interest is the total paid minus the original principal.
Extra payments
Paying extra reduces principal sooner, which reduces the interest charged on later months and shortens the term.
Sources
OpenStax, Principles of Finance. Time value of money, annuities and loan amortization (the payment formula). Book-level citation; not checked against a specific section.