Loan Calculator

Always enter 0 for the unknown value (and reenter 0 after changes).

Note - You must enter 0 for the value you want the calculator to compute.

Why does the calculator not automatically recalculate the last unknown value?

The calculator is designed to generate a payment schedule that matches the loan terms you specify. This behavior is intentional. There is no single “correct” loan payment amount—the payment is valid as long as both the lender and the borrower agree to it. If the calculator always recalculated the last unknown, that flexibility would not be possible.

About the loan origination date (start date) and the first payment due date.

Important - The first loan payment period is rarely equal in length to the regular payment frequency. For example, if the schedule is monthly, the time from loan origination (when the borrower receives the funds) to the first payment due date is usually not exactly one month. The first period is often either longer or shorter.

A longer or shorter first period directly affects the interest calculation.

Very few online calculators handle this detail correctly. For accurate interest and payment results, you must be able to set the loan origination date and the first payment due date independently. You can do this on the Options tab.

Warning - Selecting dates may produce payment amounts and interest charges that do not match the results from other calculators.

This difference is intentional.

If you want results that match other calculators, set the Loan Date and First Payment Due so that the time between them equals one full payment period as defined in Payment Frequency. Example: If the Loan Date is May 15 and the Payment Frequency is Monthly, then set the First Payment Due to June 15. This will produce a conventional interest calculation.

See Long Period Options and Short Period Options below for additional details about payment amounts and interest calculations.

Keeping it simple - If you only need estimates and not precise accuracy, you can leave the dates as they are when the calculator loads.

The four required values

• Loan Amount — the principal borrowed, not including interest.
• Number of Payments (term) — the Payment Frequency determines the loan term. For a five-year loan with monthly payments, enter 60 for the number of payments (60 months = 5 years).
• Annual Interest Rate — the nominal annual interest rate. (If a lender quotes anything other than an annual rate, consider avoiding the loan.)
• Payment Amount — the amount due on each payment date.

Set one of the above values to 0 if it is unknown.

How much can I borrow?

1. Set the loan amount to 0.
2. Enter the number of payments.
3. Enter the annual interest rate.
4. Enter the desired or expected payment amount.
5. Click Calc.

How long will it take to pay off a loan?

1. Enter the loan amount.
2. Set the number of payments to 0.
3. Enter the annual interest rate.
4. Enter the desired or expected payment amount.
5. Click Calc.

What interest rate allows me to pay $350 per month?

1. Enter the loan amount.
2. Enter the number of payments.
3. Set the annual interest rate to 0.
4. Enter $350 for the payment amount.
5. Click Calc.

Three loan options you usually do not need to change

• Payment Frequency — how often payments are scheduled. The calculator supports 11 options, including biweekly (every two weeks), monthly, and annually. Payment due dates are calculated from the first payment date.
• Compounding — in most cases, set the compounding frequency equal to the payment frequency. This produces periodic interest. Selecting Exact/Simple results in exact-day simple interest.
• Amortization Method — leave this set to Normal unless you have a specific reason to change it. For a full explanation of available methods, see Nine Loan Amortization Methods.

Results — Loan Summary

• Total Interest — total interest paid over the loan term, assuming payments are made as scheduled.
• Total Prepaid Principal — the sum of all extra payments. The payment schedule also reports the interest saved.
• Total Principal & Interest — the loan amount plus interest. This is the total cost of the loan.

Eleven advanced loan options

• Loan Date — the date funds are disbursed. For vehicle or home loans, this is the closing date.
• First Payment Due — for leases, this may be the same as the loan date. See “About the loan origination date (start date) and the first payment due date” above.
• Extra Payment Amount — enter the amount if you plan to make one or more extra payments.
• Extra Payments Start — enter the date when extra payments should begin. This does not have to match payment due dates. For example, if regular payments are due on the 1st, you could schedule extra payments on the 15th to align with your pay periods.
• Extra Payment Frequency — how often you plan to make extra payments. For example, annually when receiving a year-end bonus.
• Number of Extra Payments — enter any whole number. To continue extra payments until the loan is paid off, enter U for “Unknown.”
• Days Per Year — choose 360 or 365. Also called the day-count convention, this affects interest calculations when compounding is based on days (daily, exact/simple, or continuous) or when an initial irregular period creates odd days.
• Rounding Options — because payment and interest amounts are rounded each period (e.g., 345.0457 becomes 345.05), most loan schedules require a final rounding adjustment to bring the balance to zero. The payment schedule includes a footnote showing the rounding amount.
• Long Period Options (odd-day interest) — controls how interest is shown when the first period is longer than the selected payment frequency.
• Short Period Options — controls how payments are adjusted when the first period is shorter than the selected payment frequency.
• Fiscal Year-End — defines the fiscal year for reporting totals. Use this if your fiscal year does not match the calendar year.

More details about odd-day and irregular-period interest settings

Term Equation — Calculate the Number of Payments (N)

Variable Definitions

R

Nominal annual interest rate (the quoted rate).

n

Number of compounding or payment periods per year.

i

Periodic interest rate.

A

Loan amount (principal).

P

Amount of each equal payment.

N

Total number of payments (loan term).

Calculation Steps Explained — Fig. 2

How do you calculate the number of payments required to repay a loan?

To calculate the number of payments needed to repay a loan, apply the loan amortization formula with logarithmic operations. This method assumes fixed periodic payments and a constant interest rate. The following example illustrates the process:

1. Calculate the periodic interest rate by dividing the annual rate R = 6% by the number of periods per year n = 12: i = 0.005.
2. Substitute the values into the repayment formula: N = -ln(1 - iA/P) ÷ ln(1 + i), where A = 50,000, P = 1,000, and i = 0.005.
3. Evaluate the ratio: iA/P = (0.005 × 50,000) ÷ 1,000 = 0.25. Thus, 1 - 0.25 = 0.75.
4. Compute the natural logarithm: ln(0.75) ≈ -0.2876820724…. Apply the negative sign: -ln(0.75) ≈ 0.2876820724….
5. Evaluate the denominator: ln(1.005) ≈ 0.0049875415….
6. Divide the values: N ≈ 0.2876820724… ÷ 0.0049875415… ≈ 57.6801….
7. Round to the nearest whole payment period: N ≈ 58.

This means 58 monthly payments of $1,000 are required to repay a $50,000 loan at a 6 % annual interest rate, compounded monthly.

Step-by-step Solution – Fig. 2

1. i = 0.06 ÷ 12 = 0.005
2. N = -ln(1 - (0.005 × 50,000 ÷ 1,000)) ÷ ln(1.005)
3. = -ln(1 - 0.25) ÷ ln(1.005)
4. = -ln(0.75) ÷ ln(1.005)
5. ≈ -(-0.2876820724…) ÷ 0.0049875415…
6. ≈ 0.2876820724… ÷ 0.0049875415…
7. ≈ 57.6801…
8. ≈ 58

Final Answer

The final answer (N) is approximately 57.6801…. Because partial payment periods are not possible, we round up to 58.

Validate the calculator. $50,000 loan at 6 % annual rate with $1,000 monthly payments.

Loan Amount Equation — Calculate the Amount You Can Borrow (PV)

Variable Definitions

R

Nominal annual interest rate (the quoted annual rate).

i

Interest rate per period (R divided by f).

f

Number of payment periods per year.

n

Total number of payments for the loan or investment.

PMT

Amount of each equal periodic payment.

PV

Loan amount, or present value — the amount you can borrow.

Calculation Steps Explained — Fig. 4.

How do you calculate how much you can borrow based on a fixed payment?

To determine the loan amount you can borrow when the monthly payment, interest rate, and loan term are known, use the present value formula for an ordinary annuity. The process with example values is as follows:

1. Compute the periodic rate from the annual rate: i = R ÷ f = 0.06 ÷ 12.
2. Evaluate the periodic rate: i = 0.005.
3. Substitute into the formula: PV = 1,000 × [(1 − (1 + 0.005)−60) ÷ 0.005].
4. Simplify the base inside the exponent: 1 + 0.005 = 1.005. Result: PV = 1,000 × [(1 − (1.005)−60) ÷ 0.005].
5. Evaluate the power term: (1.005)−60 ≈ 0.741372196….
6. Subtract from 1 and divide by the rate: (1 − 0.741372196…) ≈ 0.258627804…; then ÷ 0.005.
7. Evaluate the bracketed factor: ≈ 51.7255608….
8. Multiply by 1,000 to obtain the unrounded present value: ≈ 51,725.5608….
9. Round to cents for currency reporting: PV ≈ $51,725.56.

This result means that a borrower making 60 monthly payments of $1,000 at a 6 % annual interest rate, compounded monthly, could borrow approximately $51,725.56.

Step-by-step Solution – Fig. 4

1. i = 0.06 ÷ 12
2. = 0.005
3. PV = 1,000 × [(1 − (1 + 0.005)−60) ÷ 0.005]
4. = 1,000 × [(1 − (1.005)−60) ÷ 0.005]
5. ≈ 1,000 × [(1 − 0.741372196…) ÷ 0.005]
6. ≈ 1,000 × [0.258627804… ÷ 0.005]
7. ≈ 1,000 × 51.7255608…
8. ≈ 51,725.5608…
9. ≈ 51,725.56

Final Answer

The final answer for the loan amount (PV) is approximately 51,725.56.

Validate the calculator. 60-month loan at 6 % annual rate with $1,000 monthly payments.

Annual Interest Rate Equation — Calculate the Interest Rate (R) for a Loan

Variable Definitions

PMT

The fixed payment amount.

n

Total number of payments (loan term).

P

Loan principal (initial borrowed amount).

f

Number of payments per year (payment frequency).

r

Periodic interest rate (decimal form).

R

Nominal annual interest rate (percentage).

Calculation Steps Explained — Fig. 6

How do you calculate the interest rate based on known payment and loan values?

To calculate the periodic interest rate from known loan terms, use the present value formula and apply an iterative method such as Newton–Raphson. This method refines the interest rate until the calculated loan value matches the target. Example:

1. Set up the net present value equation using the annuity factor: NPV(r) = 938.99 × (1 − (1+r)−60)/r − 50,000.
2. Choose an initial guess for the rate: r₀ = 0.005.
3. Evaluate the annuity factor at r₀: ((1 − (1+r₀)−60)/r₀) ≈ 51.7255607511….
4. Form the residual at r₀: f(r₀) ≈ 938.99 × 51.7255607511… − 50,000.
5. Compute: ≈ 48,569.7842897054… − 50,000.
6. Residual: ≈ −1,430.2157102946….
7. Evaluate the derivative at r₀: f′(r₀) ≈ −1,401,824.5767294535….
8. Apply Newton’s update: r₁ = r₀ − f(r₀)/f′(r₀) ≈ 0.0039797470….
9. Evaluate the annuity factor at r₁: ((1 − (1+r₁)−60)/r₁) ≈ 53.2803574944….
10. Residual: f(r₁) ≈ 938.99 × 53.2803574944… − 50,000.
11. Compute: ≈ 50,029.7228836692… − 50,000.
12. Residual: ≈ 29.7228836692….
13. Derivative: f′(r₁) ≈ −1,460,553.6747891533….
14. Next update: r₂ = r₁ − f(r₁)/f′(r₁) ≈ 0.0040000974….
15. Evaluate annuity factor at r₂: ((1 − (1+r₂)−60)/r₂) ≈ 53.2487163871….
16. Residual: f(r₂) ≈ 938.99 × 53.2487163871… − 50,000.
17. Compute: ≈ 50,000.0122003501… − 50,000.
18. Residual: ≈ 0.0122003501….
19. Derivative: f′(r₂) ≈ −1,459,354.8371115437….
20. Next update: r₃ = r₂ − f(r₂)/f′(r₂) ≈ 0.0040001058….
21. Evaluate annuity factor at r₃: ((1 − (1+r₃)−60)/r₃) ≈ 53.2487033941….
22. Residual: f(r₃) ≈ 938.99 × 53.2487033941… − 50,000.
23. Compute: ≈ 50,000.00000000206… − 50,000.
24. Residual: ≈ 0.000000002058….
25. Derivative: f′(r₃) ≈ −1,459,354.3448535450….
26. Final Newton correction: r ≈ r₃ − f(r₃)/f′(r₃) ≈ 0.004000105796….
27. Convert to nominal annual rate: R = r × 12 ≈ 0.04800126955….
28. Express as a percentage (to four decimals): R ≈ 4.8001 %.

This result shows that the loan carries a nominal annual interest rate of approximately 4.8001 %, based on 60 monthly payments of $938.99 to repay $50,000.

Step-by-step Solution – Fig. 6

1. NPV(r) = 938.99 × (1 − (1+r)−60)/r − 50,000
2. r₀ = 0.005
3. ((1 − (1+r₀)−60)/r₀) ≈ 51.7255607511…
4. f(r₀) ≈ 938.99 × 51.7255607511… − 50,000
5. ≈ 48,569.7842897054… − 50,000
6. ≈ −1,430.2157102946…
7. f′(r₀) ≈ −1,401,824.5767294535…
8. r₁ = r₀ − f(r₀)/f′(r₀) ≈ 0.0039797470…
9. ((1 − (1+r₁)−60)/r₁) ≈ 53.2803574944…
10. f(r₁) ≈ 938.99 × 53.2803574944… − 50,000
11. ≈ 50,029.7228836692… − 50,000
12. ≈ 29.7228836692…
13. f′(r₁) ≈ −1,460,553.6747891533…
14. r₂ = r₁ − f(r₁)/f′(r₁) ≈ 0.0040000974…
15. ((1 − (1+r₂)−60)/r₂) ≈ 53.2487163871…
16. f(r₂) ≈ 938.99 × 53.2487163871… − 50,000
17. ≈ 50,000.0122003501… − 50,000
18. ≈ 0.0122003501…
19. f′(r₂) ≈ −1,459,354.8371115437…
20. r₃ = r₂ − f(r₂)/f′(r₂) ≈ 0.0040001058…
21. ((1 − (1+r₃)−60)/r₃) ≈ 53.2487033941…
22. f(r₃) ≈ 938.99 × 53.2487033941… − 50,000
23. ≈ 50,000.00000000206… − 50,000
24. ≈ 0.000000002058…
25. f′(r₃) ≈ −1,459,354.3448535450…
26. r ≈ r₃ − f(r₃)/f′(r₃) ≈ 0.004000105796…
27. R = r × 12 × 100 ≈ 4.800126955…
28. R ≈ 4.8001 %

Final Answer

The final answer for the annual interest rate (R) is approximately 4.8001 %.

Validate the calculator. $50,000 loan with $938.99 monthly payments for a 60-month term.

Payment Amount Equation — Calculate the Periodic Payment Amount

For step-by-step guidance on solving the payment equation, seeAmortization Schedule — Payment Calculation Steps.

Amortization Equation — Calculate the Amortization Schedule

For step-by-step guidance on solving this equation, seeAmortization Schedule — Calculation Steps.