Data Source and Methodology
This calculator implements the standard fixed-rate amortization method widely used in finance education and industry. See also authoritative primers such as OpenStax Business Mathematics (Amortized Loans) and the CFPB explainer on amortization for consumer guidance. These references ground the formulas and definitions used here.
The Formula Explained
Monthly rate: \( i = \text{APR}/100/12 \)
Number of payments: \( n = 12 \times \text{years} + \text{months} \)
Monthly payment (for \( i > 0 \)): \( M = PV \cdot \dfrac{i}{1 - (1+i)^{-n}} \).
Zero-interest case: \( M = PV / n \).
Number of payments: \( n = 12 \times \text{years} + \text{months} \)
Monthly payment (for \( i > 0 \)): \( M = PV \cdot \dfrac{i}{1 - (1+i)^{-n}} \).
Zero-interest case: \( M = PV / n \).
Glossary of Terms
- Loan Amount (PV): Principal borrowed.
- APR: Annual percentage rate (nominal); converted to a monthly rate.
- Term: Total months over which the loan is repaid.
- Monthly Payment (M): Principal and interest only (P&I), excluding escrow items.
How It Works: A Step-by-Step Example
Borrow \( \$200{,}000 \) at 5% APR for 30 years (\( n = 360 \)). The monthly rate is \( i = 0.05/12 \). Using the formula:
\( M = 200000 \cdot \dfrac{0.05/12}{1 - (1+0.05/12)^{-360}} \approx \$1{,}073.64 \).
Total paid \( \approx \$1{,}073.64 \times 360 = \$386{,}511 \); Total interest \( \approx \$186{,}511 \).
Total paid \( \approx \$1{,}073.64 \times 360 = \$386{,}511 \); Total interest \( \approx \$186{,}511 \).
Frequently Asked Questions (FAQ)
Are taxes, insurance, or PMI included?
No. This tool models principal and interest (P&I) only for clarity and comparability.
Can results differ from my lender’s disclosure?
Minor differences can arise from daily interest methods, posting dates, rounding to the cent, or added fees.
Does this support extra payments?
Use our Mortgage Payoff Calculator to model monthly extras or lump-sum prepayments.