2026-08-07 9 min

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
$
Interest rate
%
Compound
Pay back
Years to repay years
Extra payment/mo
$
Results update live as you type
Repayment Summary
Loan Amount$200,000.00
Periodic Payment$1,264.14
Total Paid$455,088.98
Total Interest$255,088.98
# of Payments360

Principal vs Interest

Principal
43.9%
Interest
56.1%

Balance Over Time

30 years 0 months schedule
Amortization Schedule
#PaymentInterestPrincipalBalance
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

Normal

Periodic Payment

$1,264.14per monthly

Payment each period needed to amortize the loan

Total Interest

$255,088.98

All interest charged across the schedule

Total Paid

$455,088.98

Principal plus total interest

Number of Payments

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

200,000Principal
255,089Interest

Total Cost Breakdown

Principal44%
Interest56%

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.

EAR = (1 + r / c)^c − 1; i = (1 + EAR)^(1/p) − 1; PMT = P × i / (1 − (1 + i)^−n)

Alternative Form

n = −ln(1 − P·i / PMT) / ln(1 + i)

Variables

SymbolNameUnitDescription
PLoan amountUSDPrincipal borrowed
rNominal annual rate%Rate stated before any compounding
cCompounds per yeartimesHow often interest accrues
pPayments per yeartimesHow often you pay each year
iPeriodic ratedecimalEffective rate per payment period
nNumber of paymentsperiodsTotal term in periods
PMTPeriodic paymentUSDFixed 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.

Step 1

Enter the loan amount and the nominal interest rate.

P = loan amount; r = annual rate %
Amount:$200,000.00
Rate:6.5%
Intermediate: $200,000.00 at 6.50%
Result: Principal = $200,000.00
Step 2

Convert the nominal rate to the effective annual rate from the compound frequency.

EAR = (1 + r / c)^c − 1
Compounds / year:12
Frequency:Monthly
Intermediate: Monthly compounding → EAR
Result: EAR = 6.6972%
Step 3

Scale the EAR down to the rate actually charged each payment period.

i = (1 + EAR)^(1/p) − 1
Payments / year:12
Frequency:Monthly
Intermediate: Per-monthly rate = 0.5417%
Result: Periodic rate 0.5417%
Step 4

Solve for the payment that fully amortizes the loan in the fixed term.

PMT = P × i / (1 − (1 + i)^−n)
Payment:$1,264.14
Payments:360
Intermediate: Monthly payment known from term
Result: Payment $1,264.14
Step 5

Build the amortization schedule, applying interest then principal each period.

interest = balance × i; balance = balance − (payment − interest)
Accrued periods:360
Intermediate: Interest accumulates to $255,088.98
Result: Total paid $455,088.98 over 30 years 0 months
Step 6

The schedule is the full plan; extra payments would shorten it further.

—
Intermediate: No extra payment entered
Result: Final balance reaches zero at $0.00
Final Answer
$1,264.14

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

Principal:$200,000
Rate:6.5%
Term:30 years
Compounds:Monthly

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

▸Sizing a mortgage, auto, or personal loan payment against a budget
▸Finding out how long a set monthly payment takes to clear a balance
▸Comparing daily, monthly, and annual compounding on one loan
▸Quantifying the value of biweekly or extra-principal payments
▸Seeing the interest vs principal split at any point in the schedule

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

Myth: A lower rate is always cheaper.
Truth: A longer term can multiply the total interest even at a lower rate — the term is as important as the rate.
Myth: Monthly and annual compounding are the same.
Truth: Annual compounding charges interest only once a year; monthly compounding charges twelve times, raising the true cost slightly.
Myth: Extra payments only shrink the term.
Truth: They also cancel future interest, because each saved principal dollar removes a line of interest from every later row.

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

Mismatching the compound and payment frequencies
Use your contract’s real cadence so the effective rate is correct.
Handling extra payments as after-thoughts
Model extra as actual extra principal in the extra field; apply it every period.
Forgetting the last payment adjustment
The schedule recomputes a final balancing row so the balance hits zero exactly.
Treating the fixed-payment term as set in stone
Any payment or rate change shifts it; recompute liberally.
Reading a single number as the whole cost
Total paid includes principal plus interest — compare the full total, not just the rate.

Assumptions

This calculator makes the following assumptions to provide estimates:

Constant rate: The annual nominal rate is fixed for the term.
Standard amortization: Each payment hits interest first, then principal, on the outstanding balance.
On-time payments: No late fees or missed periods are modeled.
Contract frequency: Effective rate derives from your compound and payment choices.
Periodic extra: Any extra payment recurs each period at the same size.

Limitations

Be aware of these limitations when using this calculator:

No fees: Origination, closing, and late fees are not included.
No variable-rate path: Interim rate changes or caps are not simulated.
No day-count base: 365 vs 360-day conventions and leap years are not modeled.
Rounded display: Output rounds to cents; lenders may round paid differently.
Educational use: Not a quote or contract — verify figures with your lender.

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?
Repaying within a fixed time means you specify the loan term and the calculator determines the payment amount needed to pay off the loan on schedule. Repaying with a fixed installment means you specify the payment amount and the calculator determines how long it will take to pay off the loan.
How does compound frequency affect my loan repayment?
Compound frequency determines how often interest is added to the principal. More frequent compounding results in slightly higher total interest over the life of the loan. For example, monthly compounding yields more interest than annual compounding at the same nominal rate.
What happens if I pay back my loan more frequently?
Paying back more frequently (e.g., biweekly instead of monthly) can reduce the total interest paid because interest accrues on a smaller principal balance for shorter periods. Each payment reduces the principal sooner, and subsequent interest calculations are based on the reduced balance.
What is an amortization schedule?
An amortization schedule is a table that shows each periodic payment on a loan, breaking it down into interest and principal portions. It also shows the remaining loan balance after each payment, helping you track how much of your payment goes toward interest versus paying down the principal over time.
Can I pay off my loan early?
Yes, most loans allow early repayment without penalty, though some contracts include prepayment penalties. Paying extra toward the principal each month reduces the total interest paid and shortens the loan term. Check your loan agreement for any restrictions on prepayment.
What is the difference between APR and interest rate?
The interest rate is the cost of borrowing the principal. APR (Annual Percentage Rate) includes both the interest rate and certain fees, such as origination fees or closing costs. APR gives a more complete picture of the true cost of a loan and is typically higher than the nominal interest rate.
How does paying extra toward principal help?
Extra principal payments permanently reduce the loan balance, which reduces the interest charged in all future periods. Even one extra payment early in the loan term can save significant interest. For example, one extra payment per year on a 30-year mortgage can shorten the term by several years.
What types of loans use simple vs compound interest?
Most consumer loans (mortgages, auto loans, student loans) use simple interest, calculated on the outstanding principal balance. Credit cards and some payday loans use compound interest, where interest accrues on previously unpaid interest. Compound interest grows faster and costs more over time.
What is the effective annual rate (EAR)?
The effective annual rate (EAR) is the actual annual rate accounting for compounding frequency. A 6% nominal rate compounded monthly has an EAR of about 6.17%. The EAR helps you compare loans with different compounding periods on an apples-to-apples basis.
How do I choose between a fixed-rate and variable-rate loan?
Fixed-rate loans have the same interest rate for the entire term, providing predictable payments. Variable-rate loans can change based on market conditions, potentially offering lower initial rates but with the risk of future increases. Choose fixed rates for stability and variable rates if you expect rates to decline or plan to repay quickly.
What is the difference between a secured and unsecured loan?
Secured loans are backed by collateral (home, car) and offer lower interest rates but risk asset loss if you default. Unsecured loans (personal loans, credit cards) have no collateral but carry higher rates due to increased lender risk. Most repayment calculators support both types.
How does loan amortization work?
Amortization spreads loan payments evenly over the term. Early payments consist mostly of interest, while later payments are mostly principal. This front-loading of interest means paying extra early in the term saves more interest than paying extra later.
What is the loan payment formula?
The standard loan payment formula is P = L × r(1+r)^n / ((1+r)^n - 1), where P is the payment, L is the loan amount, r is the periodic interest rate, and n is the total number of payments. This formula calculates the fixed payment needed to fully amortize the loan.
How does paying extra every month affect my loan?
Extra monthly payments directly reduce the principal balance, saving interest on all future payments. For a $200,000 loan at 6.5% over 30 years, adding $100/month saves over $48,000 in interest and shortens the term by nearly 6 years.
What is the difference between daily and monthly compounding?
Daily compounding calculates interest 365 times per year versus 12 times for monthly compounding. At the same nominal rate, daily compounding results in a higher effective rate. For a 6% loan, daily compounding yields about 6.18% EAR versus 6.17% for monthly compounding.
What is a balloon payment?
A balloon payment is a large lump sum due at the end of a loan term, typically used in loans with lower monthly payments during the term. Balloon loans are common in commercial real estate and some auto loans. They carry refinancing risk if you cannot make the balloon payment.
How does interest-only loan repayment work?
Interest-only loans require payments covering only the interest for a specified period, typically 5-10 years. After the interest-only period, payments increase to cover both principal and interest for the remaining term. Total interest paid is higher than a standard amortizing loan.
What is the rule of 78 for loan interest?
The Rule of 78 is a method of allocating loan interest across periods, weighted toward early payments. It is used primarily in precomputed loans and can result in higher finance charges if you pay off early. The Rule of 78 is banned or restricted in many states for consumer loans.
Can I use this calculator for car loans?
Yes, enter the car loan amount, interest rate, and term to calculate monthly payments. Auto loans typically use simple interest with monthly compounding. Adding extra monthly payments can save thousands in interest over the life of a typical 5-7 year auto loan.
How does the calculator handle leap years?
The calculator uses 365 days per year for daily compounding calculations. In leap years, daily compounding would have one additional compounding period, resulting in a very slight increase in total interest. The difference is negligible for most practical purposes.
What is negative amortization?
Negative amortization occurs when your payment is less than the interest due, causing the unpaid interest to be added to the principal balance. The loan balance grows over time instead of decreasing. This can happen with some adjustable-rate and payment-option loans.
What is the difference between a loan term and amortization period?
The loan term is the actual length of the loan until the balance is due. The amortization period is the schedule over which payments are calculated. Some loans have a 30-year amortization but a 5-10 year term, requiring a balloon payment at the end of the term.
How do prepayment penalties work?
Prepayment penalties charge a fee if you pay off a loan early, typically 1-3% of the outstanding balance or 6 months of interest. They are more common in subprime auto loans and some mortgages. Always check for prepayment penalties before signing a loan agreement.
What is the difference between nominal APR and effective APR?
Nominal APR is the simple annual rate without compounding. Effective APR accounts for compounding frequency and fees. For loans, the effective APR gives a more accurate picture of the true cost. The Truth in Lending Act requires lenders to disclose the APR.
How does the calculator determine the payoff date?
For fixed-term loans, the payoff date is the end of the specified term. For fixed-payment loans, the calculator determines how many payments of the specified amount are needed to reduce the balance to zero, iterating month by month through the amortization schedule.
What is a debt consolidation loan?
A debt consolidation loan combines multiple debts into a single loan with one monthly payment, ideally at a lower interest rate. Use the Repayment Calculator to compare your current debt payments with a consolidation loan to see potential savings and payoff timeline.
How does the calculator handle different payment frequencies?
The calculator adjusts the periodic interest rate based on the selected payment frequency (daily, weekly, biweekly, semimonthly, monthly, quarterly, semiannually, annually). More frequent payments result in faster principal reduction and less total interest.
What is the biweekly payment advantage?
Biweekly payments result in 26 half-payments per year, equivalent to 13 full monthly payments. This extra payment per year can shorten a 30-year mortgage by 4-5 years and save tens of thousands in interest without requiring a higher monthly budget.
How does the calculator calculate total interest?
Total interest is the sum of all interest charges across every payment in the amortization schedule. For fixed-term loans, it is the difference between total payments and the loan amount. The calculator computes this precisely by tracking interest on each payment.
What is the impact of refinancing on loan repayment?
Refinancing replaces your current loan with a new one at a different rate or term. A lower rate reduces monthly payments and total interest. A shorter term increases payments but saves significant interest. Use the calculator to model different refinancing scenarios.
What is the difference between simple and precomputed interest?
Simple interest is calculated on the outstanding balance each period, decreasing as you pay down principal. Precomputed interest is calculated upfront and added to the loan amount. Paying off a precomputed loan early may not reduce total interest as much as a simple interest loan.
How do I calculate the true cost of a loan?
The true cost includes the total interest paid plus all fees (origination, processing, closing costs) divided by the loan amount. Use the APR, which factors in fees, to compare loans. The Repayment Calculator shows total interest and total paid for complete cost analysis.
What is a payment holiday or forbearance?
A payment holiday temporarily suspends or reduces loan payments during financial hardship. Interest typically continues to accrue, increasing the total loan cost. Forbearance is available for federal student loans and some mortgages, but should be used sparingly.
Can I calculate graduate repayment for student loans?
Graduated repayment starts with lower payments that increase every 2 years, designed for borrowers expecting income growth. This calculator models standard fixed payments. For graduated repayment, calculate each step separately or use a specialized student loan calculator.
How does the calculator round payment amounts?
The calculator uses full precision for internal calculations and rounds displayed amounts to the nearest cent. Actual loan payments may vary slightly due to lender rounding policies. Most lenders adjust the final payment to account for any rounding differences over the term.

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Related Guides

Deepen your understanding with these educational resources.

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

Truth in Lending Act (TILA)CFPB Regulation ZFTC Credit Practices Rule

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Page Information

Last Updated:

2026-08-07

Version:

2.0.0

License:

Free to use for educational and professional purposes.