Loan Amortization Schedule Calculator

Formula

PMT = P[i(1+i)^n]/[(1+i)^n-1]; OB_k = PMT × a_{n-k}|i

Enter Values

Loan Amount ($) *

Original loan amount. For mortgages, this is home price minus down payment.

Annual Interest Rate (%) *

Fixed annual interest rate. Variable/adjustable rates will change over time, requiring recalculation.

Loan Term (years) *

Loan term in years. Common mortgage terms: 15, 20, 25, 30 years. Auto loans: 3-7 years. Personal loans: 1-5 years.

Results

Interpretation

Monthly Payment: $1,199.10 | Total Interest: $231,676.38 | Total Paid: $431,676.38. The schedule shows how early payments are mostly interest (Payment 1: $1,000 interest, $199 principal) while later payments are mostly principal (Payment 360: $5.99 interest, $1,193 principal). Outstanding balance decreases slowly at first, then accelerates.

How It Works

An amortization schedule shows the breakdown of each payment into interest and principal portions, plus the remaining balance after each payment. Early payments pay mostly interest because balance is high. As principal is reduced, interest portion decreases and principal portion increases. The schedule proves the loan will be fully paid after n payments.

Key Points

Early payments are mostly interest, later payments mostly principal.
Use to see exactly when you'll reach 20% equity (to remove PMI).
Track progress: compare actual balance to scheduled balance.
Annual summary useful for tax deductions (mortgage interest deduction).
Print schedule for refinance comparison - see breakeven point.

References

Broverman, S.A. (2015). Mathematics of Investment and Credit (6th Edition). ACTEX Publications. Chapter 3, Section 3.1.2: The Amortization Schedule (pages 82-85). Table 3.1 (page 83) shows example schedule. Formula 3.2 (page 84): I_k = OB_{k-1} × i and PR_k = R - I_k. Section 3.1.4: Prospective Outstanding Balance (pages 88-90): OB_k = R × a_{n-k}|i.