Amortization Formula
The amortization formula helps you determine the outstanding principal balance on a loan, such as a mortgage, after a specific number of payments have been made. It's crucial for understanding how much you still owe and how your equity is building over time.
Formula
Copy the exact expression or work through it step by step below.
Remaining Balance = Principal x (1 + Monthly Rate) ^ Payments Made - Monthly Payment x [((1 + Monthly Rate) ^ Payments Made - 1) / Monthly Rate] Variables
RB
Remaining Balance
The remaining balance value plugged into the amortization calculation.
P
Principal
The principal value plugged into the amortization calculation.
MR
Monthly Rate
The monthly rate assumption used in the amortization calculation.
PM
Payments Made
The recurring amount that changes the amortization result over time.
MP
Monthly Payment
The recurring amount that changes the amortization result over time.
Step By Step
- 1
Set the baseline case with the real calculator inputs.
Home Price = $420,000, Down Payment Percent = 20.0%, Annual Rate Percent = 6.50%, Loan Term Years = $30.00
- 2
Translate rates, periods, and cash values onto the same footing before combining them.
Keep the amortization assumptions consistent instead of mixing monthly and annual views.
- 3
Apply the formula and read the first calculator outputs, not just the headline assumption.
The calculator lands with estimated monthly housing cost at $2,659 and principal + interest at $2,124.
- 4
Run one changed scenario so the formula is stress-tested before it is trusted.
The mortgage payment amortization calculator page is the fastest way to compare that second case.
Worked Example
Amortization sample case
Home Price
$420,000
Down Payment Percent
20.0%
Annual Rate Percent
6.50%
Loan Term Years
$30.00
Remaining Balance = Principal x (1 + Monthly Rate) ^ Payments Made - Monthly Payment x [((1 + Monthly Rate) ^ Payments Made - 1) / Monthly Rate] using home price $420,000, down payment percent 20.0%, annual rate percent 6.50%, loan term years $30.00.
The calculator lands with estimated monthly housing cost at $2,659 and principal + interest at $2,124.
Common Variations
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Sources & References
- What Is an Amortization Schedule? — Investopedia
- Mortgage Amortization Calculator — Bankrate
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