Repayment Calculator
Estimate the monthly payment for a fixed loan term or how long it takes to clear a loan at a fixed payment. Compare compound and payment frequencies, watch an amortization schedule build, and see how extra payments shorten the term and save interest.
Calculator
| Loan Amount | $200,000.00 |
| Periodic Payment | $1,264.14 |
| Total Paid | $455,088.98 |
| Total Interest | $255,088.98 |
| # of Payments | 360 |
Principal vs Interest
Balance Over Time
| # | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $1,264.14 | $1,083.33 | $180.80 | $199,819.20 |
| 2 | $1,264.14 | $1,082.35 | $181.78 | $199,637.42 |
| 3 | $1,264.14 | $1,081.37 | $182.77 | $199,454.65 |
| 4 | $1,264.14 | $1,080.38 | $183.76 | $199,270.89 |
| 5 | $1,264.14 | $1,079.38 | $184.75 | $199,086.14 |
| 6 | $1,264.14 | $1,078.38 | $185.75 | $198,900.39 |
| 7 | $1,264.14 | $1,077.38 | $186.76 | $198,713.63 |
| 8 | $1,264.14 | $1,076.37 | $187.77 | $198,525.86 |
| 9 | $1,264.14 | $1,075.35 | $188.79 | $198,337.07 |
| 10 | $1,264.14 | $1,074.33 | $189.81 | $198,147.26 |
| 11 | $1,264.14 | $1,073.30 | $190.84 | $197,956.42 |
| 12 | $1,264.14 | $1,072.26 | $191.87 | $197,764.55 |
| 13 | $1,264.14 | $1,071.22 | $192.91 | $197,571.64 |
| 14 | $1,264.14 | $1,070.18 | $193.96 | $197,377.68 |
| 15 | $1,264.14 | $1,069.13 | $195.01 | $197,182.67 |
| 16 | $1,264.14 | $1,068.07 | $196.06 | $196,986.61 |
| 17 | $1,264.14 | $1,067.01 | $197.13 | $196,789.49 |
| 18 | $1,264.14 | $1,065.94 | $198.19 | $196,591.29 |
| 19 | $1,264.14 | $1,064.87 | $199.27 | $196,392.03 |
| 20 | $1,264.14 | $1,063.79 | $200.35 | $196,191.68 |
| 21 | $1,264.14 | $1,062.70 | $201.43 | $195,990.25 |
| 22 | $1,264.14 | $1,061.61 | $202.52 | $195,787.73 |
| 23 | $1,264.14 | $1,060.52 | $203.62 | $195,584.11 |
| 24 | $1,264.14 | $1,059.41 | $204.72 | $195,379.39 |
| 25 | $1,264.14 | $1,058.31 | $205.83 | $195,173.55 |
| 26 | $1,264.14 | $1,057.19 | $206.95 | $194,966.61 |
| 27 | $1,264.14 | $1,056.07 | $208.07 | $194,758.54 |
| 28 | $1,264.14 | $1,054.94 | $209.19 | $194,549.35 |
| 29 | $1,264.14 | $1,053.81 | $210.33 | $194,339.02 |
| 30 | $1,264.14 | $1,052.67 | $211.47 | $194,127.55 |
| 31 | $1,264.14 | $1,051.52 | $212.61 | $193,914.94 |
| 32 | $1,264.14 | $1,050.37 | $213.76 | $193,701.18 |
| 33 | $1,264.14 | $1,049.21 | $214.92 | $193,486.26 |
| 34 | $1,264.14 | $1,048.05 | $216.09 | $193,270.17 |
| 35 | $1,264.14 | $1,046.88 | $217.26 | $193,052.92 |
| 36 | $1,264.14 | $1,045.70 | $218.43 | $192,834.48 |
| 37 | $1,264.14 | $1,044.52 | $219.62 | $192,614.87 |
| 38 | $1,264.14 | $1,043.33 | $220.81 | $192,394.06 |
| 39 | $1,264.14 | $1,042.13 | $222.00 | $192,172.06 |
| 40 | $1,264.14 | $1,040.93 | $223.20 | $191,948.86 |
| 41 | $1,264.14 | $1,039.72 | $224.41 | $191,724.44 |
| 42 | $1,264.14 | $1,038.51 | $225.63 | $191,498.82 |
| 43 | $1,264.14 | $1,037.29 | $226.85 | $191,271.96 |
| 44 | $1,264.14 | $1,036.06 | $228.08 | $191,043.88 |
| 45 | $1,264.14 | $1,034.82 | $229.32 | $190,814.57 |
| 46 | $1,264.14 | $1,033.58 | $230.56 | $190,584.01 |
| 47 | $1,264.14 | $1,032.33 | $231.81 | $190,352.21 |
| 48 | $1,264.14 | $1,031.07 | $233.06 | $190,119.14 |
| 49 | $1,264.14 | $1,029.81 | $234.32 | $189,884.82 |
| 50 | $1,264.14 | $1,028.54 | $235.59 | $189,649.23 |
| 51 | $1,264.14 | $1,027.27 | $236.87 | $189,412.36 |
| 52 | $1,264.14 | $1,025.98 | $238.15 | $189,174.21 |
| 53 | $1,264.14 | $1,024.69 | $239.44 | $188,934.76 |
| 54 | $1,264.14 | $1,023.40 | $240.74 | $188,694.02 |
| 55 | $1,264.14 | $1,022.09 | $242.04 | $188,451.98 |
| 56 | $1,264.14 | $1,020.78 | $243.35 | $188,208.63 |
| 57 | $1,264.14 | $1,019.46 | $244.67 | $187,963.95 |
| 58 | $1,264.14 | $1,018.14 | $246.00 | $187,717.96 |
| 59 | $1,264.14 | $1,016.81 | $247.33 | $187,470.63 |
| 60 | $1,264.14 | $1,015.47 | $248.67 | $187,221.95 |
| ... 300 more payments |
Results
Periodic Payment
$1,264.14per monthly
Payment each period needed to amortize the loan
$255,088.98
All interest charged across the schedule
$455,088.98
Principal plus total interest
360
30 years 0 months at monthly intervals
The calculator assumes a constant nominal rate, standard month-by-month amortization, and on-time payments. Compound and payment frequencies come from your selections; actual lender figures may differ.
Visualizations
Principal vs Interest
Total Cost Breakdown
Balance Over Time — Base vs Extra
Formula
The nominal annual rate r is converted to an effective annual rate EAR with the compound frequency c, then to the per-period rate i with the payment frequency p. The fixed-time tab solves the annuity formula for the payment that zeros the balance in n periods; the fixed-payment tab inverts the equation to find n.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| P | Loan amount | USD | Principal borrowed |
| r | Nominal annual rate | % | Rate stated before any compounding |
| c | Compounds per year | times | How often interest accrues |
| p | Payments per year | times | How often you pay each year |
| i | Periodic rate | decimal | Effective rate per payment period |
| n | Number of payments | periods | Total term in periods |
| PMT | Periodic payment | USD | Fixed payment that fully amortizes the loan |
Explanation
Repayment depends on the gap between the effective periodic rate and the payment you send each period. A fixed term finds the payment; a fixed payment finds the term. Total interest is simply everything paid minus the amount borrowed, which is why matching the true compounding frequency matters.
Derivation
EAR = (1 + r/c)^c − 1 restates the nominal rate with compounding. The periodic rate i = (1 + EAR)^(1/p) − 1 gives the per-payment charge. The standard annuity payment PMT = P·i / (1 − (1 + i)^−n) fully amortizes the loan, and solving for n = −ln(1 − P·i/PMT) / ln(1 + i) handles the fixed-payment mode. Each period charges interest on the outstanding balance, then applies principal; the final period absorbs any leftover balance.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Enter the loan amount and the nominal interest rate.
Convert the nominal rate to the effective annual rate from the compound frequency.
Scale the EAR down to the rate actually charged each payment period.
Solve for the payment that fully amortizes the loan in the fixed term.
Build the amortization schedule, applying interest then principal each period.
The schedule is the full plan; extra payments would shorten it further.
Worked Examples
See how the calculator works with different scenarios.
Scenario
A $200,000 mortgage at 6.5% compounded monthly, repaid monthly over 30 years.
Inputs
Calculation
EAR = (1 + 0.065/12)^12 − 1 = 6.697% i = (1.06697)^(1/12) − 1 = 0.5417% n = 30 × 12 = 360 PMT = 200000 × 0.005417 / (1 − 1.005417^−360) = $1,264
Result
About $1,264 per month, total interest ≈ $255,000
Interpretation
Early payments are mostly interest because interest is charged on the full balance first. The fixed payment stays level, so the interest share falls steadily over the term.
Understanding Your Result
Your Result: Periodic Payment: $1,264.14 per monthly
Typical range: For a 30-year mortgage around 6.5% in 2026, expect roughly $1,264 a month per $200,000 borrowed with total interest near $255,000. Shorter terms, biweekly payments, and any extra payment compress the interest sharply.
What This Means
The results are the periodic payment (fixed term) or the payoff window (fixed payment), total interest paid, total paid, and the count of payments. The amortization schedule breaks every period into interest and principal so the trajectory of the balance is transparent.
Why It Matters
Adjusting compound and payment frequency can alter the total interest on a long loan by tens of thousands of dollars. Knowing your real per-period rate and the cost of a fixed payment is what makes device choices possible.
Professional Interpretation
Lenders underwrite using the APR (fees rolled into the rate) and disclose the effective rate. The calculated payment matches the amortization only when the compounding and payment frequencies match the actual contract.
Why compounding matters
Daily compounding yields a higher EAR than monthly at the same nominal rate. The difference is small per period but compounds across decades.
Payment frequency economics
26 biweekly payments a year equal 13 monthly payments, quietly removing a month of interest accrual each year.
Extra payments and principal
Any payment above the computed amount lands on principal, shrinking every later interest line since interest is charged on the reduced balance.
Recommendations
- •Set compound and payment frequency to your exact contract terms
- •Compare the fixed-payment tab against your true budget
- •Route any extra to principal right after the scheduled payment
- •Re-run the plan after a rate change or a large payment
- •Confirm the final payment scale with the lender
Educational Content
Introduction
A loan repayment calculator estimates either the payment needed to retire a loan in a chosen term or the term needed when the payment is fixed. It converts your nominal rate into the true effective rate your compounding and payment cadence produce, then runs the standard amortization schedule.
Concept Explanation
The engine anchors on the EAR built from compounding, converts it to the per-period rate from the payment frequency, and then solves the annuity formula. Fixed-term locks n and solves PMT; fixed-payment locks PMT and solves n. Every result is a direct consequence of the five inputs.
Applications
Benefits
- •Makes payment-vs-term trade-offs immediately visible
- •Applies the correct periodic rate for any pairing of frequencies
- •Builds a full period-by-period schedule to verify any claim
- •Answers "what if I pay $X?" without any assumptions
- •Works for mortgages, auto, personal, and student loans alike
Limitations
- •Assumes a constant rate for the whole term
- •No support for interest-only periods or balloon payments
- •Extra payments are modeled as recurring, not lump, amounts
- •Early-settlement penalties and lender rounding at the final row are out of scope
- •Educational output — for a quote, confirm with your lender
Best Practices
- •Match compound and payment frequency exactly to the contract
- •Round your payment up by a few dollars to balance the schedule
- •Make extra payments soon after the due date to shrink interest
- •Reward a good rate: stay with a low term rather than maxing length
- •Keep the fixed-payment tab handy for budget-first planning
Common Misconceptions
Practical Tips
- •Set the compound frequency to your contract — banks do not always compound monthly
- •An extra $50 a month on a big 30-year loan still saves thousands
- •Rounding your periodic payment up by a few dollars offsets final-row drift
- •If you pay biweekly, model biweekly, not monthly + dividing
- •Re-run when your rate changes so the timeline stays honest
- •The fixed-payment tab is your budget planning tool, use it first
Common Mistakes
Assumptions
This calculator makes the following assumptions to provide estimates:
Limitations
Be aware of these limitations when using this calculator:
Frequently Asked Questions
Answers to common questions about this calculator.
What is the difference between repaying within a fixed time and repaying with a fixed installment?
How does compound frequency affect my loan repayment?
What happens if I pay back my loan more frequently?
What is an amortization schedule?
Can I pay off my loan early?
What is the difference between APR and interest rate?
How does paying extra toward principal help?
What types of loans use simple vs compound interest?
What is the effective annual rate (EAR)?
How do I choose between a fixed-rate and variable-rate loan?
What is the difference between a secured and unsecured loan?
How does loan amortization work?
What is the loan payment formula?
How does paying extra every month affect my loan?
What is the difference between daily and monthly compounding?
What is a balloon payment?
How does interest-only loan repayment work?
What is the rule of 78 for loan interest?
Can I use this calculator for car loans?
How does the calculator handle leap years?
What is negative amortization?
What is the difference between a loan term and amortization period?
How do prepayment penalties work?
What is the difference between nominal APR and effective APR?
How does the calculator determine the payoff date?
What is a debt consolidation loan?
How does the calculator handle different payment frequencies?
What is the biweekly payment advantage?
How does the calculator calculate total interest?
What is the impact of refinancing on loan repayment?
What is the difference between simple and precomputed interest?
How do I calculate the true cost of a loan?
What is a payment holiday or forbearance?
Can I calculate graduate repayment for student loans?
How does the calculator round payment amounts?
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Related Guides
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Effective Annual Rate (EAR)
- The annual cost restated to include the compounding frequency.
- Periodic Rate
- The rate per payment period, (1 + EAR)^(1/p) − 1.
- Amortization
- Payment splitting into interest and principal each period.
- Annuity Formula
- The closed-form equation connecting principal, rate, term, and payment.
- Fixed Term
- You choose the term; the calculator finds the payment.
- Fixed Payment
- You choose the payment; the calculator finds the term.
- Principal
- The amount lent that must still be repaid.
- Compound Frequency
- How many times a year interest accrues on the balance.
- Payment Frequency
- How many times a year you make a payment.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
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Page Information
2026-08-07
2.0.0
Free to use for educational and professional purposes.