Mathematics & Statistics / Financial Mathematics
Amortization Schedule Calculator
Amortization Formula
Monthly Payment: M = P[r(1+r)^n] / [(1+r)^n - 1]
Where:
• P = Principal loan amount
• r = Monthly interest rate (Annual rate / 12)
• n = Total number of payments (Years × 12)
Each Payment: Interest = Balance × r, Principal = Payment - Interest
Break down each payment into principal and interest over time to understand debt payoff progression and total borrowing cost.
Formula
Payment = P * [r(1 + r)^n] / [(1 + r)^n - 1]; schedule iterates interest_t = balance_t * r
Worked Example
principal300000
annualRatePercent5.8
termYears30
Result: Fixed monthly payment with declining interest share over timeEarly payments are interest-heavy; principal share increases progressively as outstanding balance declines.
Frequently Asked Questions
Why do early payments mostly cover interest?
Interest is calculated on the larger beginning balance, so it dominates initial installments.
How do extra payments affect schedule?
Additional principal payments reduce balance faster, shorten term, and lower total interest paid.