calculate-loan

01 Loan payments

Total Loan Payment Formula and Worked Example

Calculator No. 01-6946 · Updated · Formula and assumptions shown below

Monthly payment $405.53
Total of payments
$24,331.80
= Monthly payment × loan term × 12
Total interest
$4,331.80
= Total of payments − loan amount
Loan amount
$20,000
Input
You enter
Loan amount ($), Interest rate (APR) (%), Loan term (years)
You get
Monthly payment ($), Total of payments ($), Total interest ($)
Rounding
2 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

The total loan payment formula is total paid = monthly payment × number of monthly payments; for a fixed-rate loan, calculate the monthly payment with the amortization formula first. This calculator uses the loan amount, annual APR, and term in years to show the monthly payment and total interest, from which you can find the total paid.

Formula

For a fixed-rate loan repaid with equal monthly payments, let P be the amount borrowed in dollars, a the annual APR as a percentage, and y the term in years. The number of monthly payments is n = 12y, and the monthly rate as a decimal is r = a / 1200.

The level monthly payment is:

M = round(P × r / [1 − (1 + r)−n], 2)

The total of scheduled payments is T = M × n. The total interest in this simplified calculation is I = T − P. Here, M is the monthly payment in dollars, T is total payments in dollars, and I is total interest in dollars. The payment is rounded to cents before calculating the totals, matching the calculator.

Worked Example

Using the calculator’s defaults: principal P = $20,000, APR a = 8%, and term y = 5 years.

  1. Convert the APR to a monthly decimal rate: r = 8 / 1200 = 0.0066667.
  2. Convert the term to monthly payments: n = 5 × 12 = 60.
  3. Apply the payment formula: M = round(20,000 × 0.0066667 / [1 − (1.0066667)−60], 2) = $405.53.
  4. Multiply the rounded payment by the number of payments: T = $405.53 × 60 = $24,331.80.
  5. Subtract the original principal: I = $24,331.80 − $20,000 = $4,331.80.

So the scheduled total is $24,331.80, comprising the original $20,000 borrowed and $4,331.80 in calculated interest. These totals use the rounded monthly amount; a lender’s final payment can differ slightly because of its exact payment schedule and rounding.

Assumptions

  • The interest rate stays fixed for the full term.
  • There are equal monthly payments, made at the end of each monthly period.
  • Interest accrues monthly using the APR divided by 12.
  • The calculation excludes fees, taxes, insurance, PMI, and escrow because they are not calculator inputs.

How the Total Is Built

A loan payment generally contains both interest and principal. Early in a standard amortizing loan, the outstanding balance is larger, so more of a payment goes toward interest. As the balance declines, the interest portion tends to shrink and the principal portion grows. The monthly payment can remain level even as its internal allocation changes.

That is why total loan payments are not simply the principal plus one month of interest. Interest is charged over the life of the loan according to the remaining balance and payment schedule. The amortization formula finds the level payment that pays off the principal and accumulated interest over the specified number of periods, assuming the stated rate and timing.

When to Use This Calculation

Use the formula to estimate scheduled payments and the sum of those payments when you know the amount financed, APR, and term. It can also help explain why a longer term may produce a smaller monthly payment but a larger total interest amount when the rate and principal are held constant: the balance remains outstanding for more periods.

Use the amount actually financed, not necessarily the item’s advertised price. If a loan adds financed charges or includes a down payment, the principal used in the formula should reflect the amount borrowed. For a variable-rate loan, the result is only a fixed-rate illustration; future payments can change if the rate changes.

Common Mistakes and Limits

  • Mixing annual and monthly rates: The formula needs a monthly decimal rate. With APR entered as a percentage, divide by 1,200—not 12—to convert, for example, 8% to 0.0066667 per month.
  • Mixing years and months: This calculator accepts years and multiplies by 12. If using a version that accepts months, enter the total number of monthly periods instead.
  • Rounding too early: Rounding the monthly payment to cents before multiplying gives the displayed total. Calculations that keep extra decimals until the end can produce a slightly different figure.
  • Confusing payment total with payoff cost: The total here is the sum of scheduled payments. It does not include optional extra payments, late charges, or other amounts not entered.

The standard formula assumes equal periodic payments and a fixed rate. It does not model irregular payment dates, daily interest calculations, payment holidays, balloon amounts, changing rates, or a final installment adjusted for rounding. If a lender’s disclosed schedule uses different conventions, its figures may not match this estimate.

Frequently Asked Questions

How do I calculate total loan payments?
Find the monthly payment using the fixed-rate amortization formula, then multiply that payment by the number of monthly payments. To estimate interest, subtract the original principal from the total.

Is total loan payment the same as total interest?
No. Total payments include repayment of principal as well as interest. In this calculation, total interest equals total payments minus the amount borrowed.

Does the total include fees and insurance?
No. This calculator uses principal, APR, and term only. Add any relevant costs separately using the figures provided in the loan disclosure; taxes, insurance, PMI, escrow, and fees are not modelled here.

Why can my lender’s total differ from this result?
The lender may use different payment dates, interest accrual or rounding conventions, or include charges that are outside this formula. Compare the inputs and payment schedule with the lender’s disclosure.

Can I use this formula for a variable-rate loan?
It can estimate payments for a period under an assumed fixed rate, but it cannot predict later payments if the rate changes. Recalculate using updated terms when the applicable rate or schedule changes.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

Formula used
in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out tot | Total of payments | $ | pmt * yrs * 12 | 2
out int | Total interest | $ | tot - p | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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