Amortization Balance Calculator
Solve for the remaining balance on an amortizing loan, or back-solve for the principal, rate, payment, or number of payments — with a payoff curve, a loan-setup builder, and reference tables.
Principal — scales everything
A larger original loan produces a proportionally larger balance at any given point, all else equal.
Rate — compounds against you
A higher periodic rate means more of each payment covers interest rather than principal, so the balance falls more slowly.
Payment — the main lever you control
A higher payment accelerates payoff disproportionately, since extra dollars go straight to principal once interest is covered.
Payments made — a non-linear curve
Balance drops slowly at first (most of each early payment is interest) and accelerates near the end of the term — the classic amortization curve.
Loan Setup Builder & Reference Tables
Turn an annual rate and loan term into the periodic rate and payment this calculator needs, and see milestones along the amortization schedule.
Build PMT and r from loan terms
Balance at Amortization Milestones
Computed live from your current P, r, and PMT above.
| % of full payoff horizon | Payments made | Remaining balance | % of principal paid off |
|---|
Approximate Monthly Rate by Annual Rate
| Annual rate (APR) | Monthly periodic rate |
|---|---|
| 3% | 0.25% |
| 5% | 0.4167% |
| 6% | 0.5% |
| 7.5% | 0.625% |
| 10% | 0.8333% |
How to Use This Calculator
The remaining-balance formula links five quantities: principal, periodic rate, payment, number of payments made, and the resulting balance.
Choose what to solve for
Pick B, P, r, PMT, or p — the tool rearranges the formula automatically, including a numerical solve for r.
Build from real loan terms
Use the loan builder to turn an annual rate, term, and payment frequency into the periodic rate and payment.
Enter values or use presets
Rate and payment-count presets cover common APRs and loan milestones.
Read the payoff curve
The chart shows the balance declining over the life of the loan, with your point marked.
Check amortization milestones
See the balance and percent paid off at 25%, 50%, 75%, and 100% of the full payoff horizon.
Go Advanced
Adds sensitivity and companion metrics like interest paid to date and payments remaining.
What This Tool Offers
Solve any variable
Compute balance, principal, rate, payment, or payments made.
Loan setup builder
Convert an annual rate and term into the periodic rate and payment.
Payoff curve chart
Visualize the full amortization schedule, not just one snapshot.
Milestone table
Balance and percent paid off at key points in the loan term.
Companion metrics
Interest paid to date, principal paid down, and payments remaining.
Sensitivity check
See how a 1% change in an input moves the result.
What Does This Remaining-Balance Formula Measure?
For a standard fixed-payment, fixed-rate amortizing loan, this formula gives the outstanding balance after any number of payments, without needing to compute every intervening payment one at a time.
P = [B + PMT·((1+r)^p−1)/r] / (1+r)^p
PMT = r·[P(1+r)^p − B] / [(1+r)^p − 1]
p = ln[ (B − PMT/r) / (P − PMT/r) ] / ln(1+r)
Frequently Asked Questions
Both must match the same payment frequency — if payments are monthly, r should be the monthly rate (commonly annual rate ÷ 12) and PMT the monthly payment. Mixing frequencies gives an incorrect balance.
Early in the loan, most of each payment covers interest on the large remaining balance. As the balance shrinks, a growing share of each payment goes to principal — the balance falls faster near the end of the term.
It works for standard fixed-rate, fixed-payment loans like typical mortgages, auto loans, and personal loans. It doesn't model adjustable rates, interest-only periods, or loans with irregular extra payments.
Not in closed form — this tool solves for it numerically (bisection) over a wide range of plausible periodic rates.
If PMT is less than or equal to the interest due each period (P×r), the balance never decreases — this is negative amortization, and the tool will flag it rather than show a payoff date.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| B | Remaining balance | currency |
| P | Original loan principal | currency |
| r | Periodic interest rate | |
| p | Number of payments made | |
| PMT | Fixed periodic payment | currency |
What it means
This formula calculates the remaining balance of a loan after a certain number of payments (p) have been made. It is derived from the amortization formula. It is useful for understanding how much principal remains, for refinancing decisions, and for early payoff calculations. It helps borrowers see the impact of extra payments on the loan term and interest savings. Understanding this calculation is important for effective debt management and financial planning.
Worked example
Remaining Loan Balance – Two Real-World Examples
Real-WorldA homeowner borrows $300,000 for 30 years at 6.5% annual interest. After making 60 monthly payments (5 years), they want to know how much principal is still owed before considering a refinance or estimating home equity.
| Parameter | Value |
|---|---|
| Original Principal | $300,000 |
| Annual Interest Rate | 6.5% |
| Loan Term | 30 years |
| Payments Made | 60 |
| Monthly Payment | $1,896.20 |
B = 300000 × (1.0054167)60 − 1896.20 × [(1.0054167)60 − 1] ÷ 0.0054167
A buyer finances a $25,000 car at 7% annual interest for 5 years. After 24 payments (2 years), they want to estimate the outstanding loan balance before trading in the vehicle.
| Parameter | Value |
|---|---|
| Original Principal | $25,000 |
| Annual Interest Rate | 7% |
| Loan Term | 5 years |
| Payments Made | 24 |
| Monthly Payment | $495.00 |
B = 25000 × (1.0058333)24 − 495 × [(1.0058333)24 − 1] ÷ 0.0058333
Common mistakes
- Remaining balance: The outstanding loan balance after a certain number of payments (p).
- P: Original loan amount.
- r: Monthly interest rate (in decimal).
- PMT: The fixed monthly payment.
- p: The number of payments already made – not the total number.
- Formula: This is the standard amortization formula – ensure you use the same interest rate per period.
Applications
The remaining loan balance formula gives the unpaid principal after a certain number of payments (p) in an amortising loan. This is used for tracking loan progress, for evaluating refinancing opportunities, and for assessing early payoff options. Borrowers can use it to see how much principal remains and to plan extra payments. Lenders use it for servicing and for calculating interest accrual. By understanding the remaining balance, individuals can make informed decisions about extra payments, refinancing, and debt management. This formula is also useful for calculating equity in a mortgaged property. It is a key tool in loan management and financial planning.
- Mortgage balance tracking and equity calculation
- Refinancing decision analysis
- Early payoff planning and extra payment strategies
- Loan servicing and amortisation schedules
- Personal debt management and tracking
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