Total Cost Formula for a Loan

The total cost formula for a fixed-rate installment loan is total cost = monthly payment × number of monthly payments; if you mean the amount paid above the amount borrowed, total interest = total cost − loan amount. Enter the loan amount, annual percentage rate (APR), and term to estimate the monthly payment and total interest.

Formula

For a loan with equal monthly payments, calculate the payment using the standard amortizing-loan formula, then multiply that rounded payment by the number of payments to find the total paid. Subtract the original principal to find the interest portion.

• Monthly payment: M = P × r / [1 − (1 + r)⁻ⁿ]
• Total paid: T = M × n
• Total interest: I = T − P

Here, P is the amount borrowed in dollars; APR is the annual percentage rate entered as a percentage; r = APR / 1200 is the monthly rate expressed as a decimal; n is the number of monthly payments, equal to years × 12; M is the monthly payment in dollars; T is total payments in dollars; and I is total interest in dollars. The calculator rounds M to cents before calculating I, so its totals use the displayed payment.

Worked Example

Using the calculator’s default values, the loan amount is $20,000, APR is 8%, and the term is 5 years. There are 5 × 12 = 60 payments, and the monthly rate is 8 / 1200 = 0.0066667.

1. Substitute into the payment formula: M = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰].
2. The monthly payment is approximately $405.53 after rounding to cents.
3. Total interest is $405.53 × 60 − $20,000 = $4,331.80.

The displayed outputs are therefore a monthly payment of $405.53 and total interest of $4,331.80. Total payments are $24,331.80. The figures use the rounded monthly payment, rather than an unrounded internal payment, to keep the calculation consistent with the calculator’s stated method.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and made at the end of each payment period.
• Interest compounds monthly at APR / 12.
• The calculation excludes fees, taxes, insurance, PMI, escrow, late charges, and any other amounts not entered as inputs.

What Total Cost Includes

“Total cost” can refer to different quantities, so check what a source or calculator means by the phrase. In this page, total payments means the sum of the scheduled loan payments. Total interest means the part of those payments above the original principal. Neither figure necessarily represents every expense connected with borrowing.

For instance, an upfront fee may increase the cash needed to obtain a loan without appearing in the payment formula. A loan disclosure may also show costs or payment details that this basic estimate does not model. To estimate a broader out-of-pocket amount, identify the costs relevant to the transaction and add them separately; do not treat them as interest unless they are actually financed and accrue interest.

How the Formula Works

Each monthly payment covers interest accrued since the previous payment and reduces the remaining principal. Early in a fully amortizing loan, the balance is larger, so more of a level payment goes toward interest. As the balance falls, the interest portion generally shrinks and more of each payment reduces principal. The payment formula accounts for this changing split while keeping the scheduled payment level.

Multiplying the payment by the number of payments gives the scheduled sum across the full term. Subtracting the original principal isolates the interest paid under these assumptions. A longer term usually means more payment periods, and therefore can produce more total interest even when the monthly payment is lower. The result depends on the specific principal, rate, and term entered; it is not a comparison of current market offers.

When to Use It and Common Mistakes

This formula is useful for understanding the arithmetic behind a fixed-rate loan estimate, checking the relationship between payment and total interest, or comparing hypothetical combinations of principal, APR, and term. For an actual loan, use the exact figures supplied by the lender and check whether the quoted payment includes any other charges.

• Confusing interest with total paid: total paid includes repayment of the principal; interest is only the amount above principal.
• Entering APR in the wrong units: enter 8 for 8%, not 0.08. The formula converts the percentage into a monthly decimal rate.
• Mixing years and months: this calculator takes a term in years and converts it to months. A five-year term means 60 monthly payments.
• Rounding at different stages: the calculator rounds each scheduled payment to cents and uses that rounded amount in total interest. A lender’s final schedule may differ slightly because of its exact dates and rounding practices.
• Assuming every borrowing cost is included: this estimate does not add fees, insurance, taxes, or other costs unless those are incorporated in the inputs.

Limits and Related Questions

The formula assumes a fixed APR, a fully amortizing balance, and regular monthly payments. It does not model changing rates, skipped or irregular payments, extra principal payments, deferred interest, balloon payments, or a payoff before the end of the term. It also treats APR as the rate used for monthly interest calculation; actual loan terms and payment schedules may require different details. The APR and any other real loan figures should be obtained from the lender rather than inferred from this example.

Frequently Asked Questions

What is the total cost formula?
Total scheduled payments = monthly payment × number of payments. For a fully amortizing fixed-rate loan, total interest = total scheduled payments − principal borrowed.

Is total cost the same as total interest?
No. Total payments include repayment of the borrowed principal as well as interest. Total interest is the excess of scheduled payments over principal under the stated assumptions.

How do I calculate the monthly payment first?
Use M = P × r / [1 − (1 + r)⁻ⁿ], where P is principal, r is APR divided by 1,200, and n is the number of monthly payments. Round the result to cents when estimating a payment in dollars.

Does the total include loan fees?
Not in this calculator. It estimates scheduled payments and interest from the entered principal, APR, and term; fees and other costs must be checked separately in the lender’s documents.

Why can a longer loan term have a higher total cost?
A longer term has more monthly payment periods. Even if its monthly payment is smaller, interest can accrue over more periods, increasing total interest for the same principal and rate.

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

Related

• Loan Amortization Calculator With Escrow Explained
• Loan Calculator Payment With Escrow: What It Includes
• Loan Total Cost Calculator: Payments and Interest

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 | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2