Total Cost Equation for a Loan

The total cost equation for a fixed-payment loan is total cost = monthly payment × number of payments; if “cost” means the amount paid above the amount borrowed, total interest = total cost − loan principal. Enter the loan amount, APR, and term to estimate the monthly payment and total interest.

Formula

For a fixed-rate loan with equal monthly payments, the equations are:

• Monthly payment: M = round[P × r / (1 − (1 + r)⁻ⁿ), 2]
• Total of payments: T = M × n
• Total interest: I = T − P

P is the principal, or amount borrowed, in dollars. APR is the annual percentage rate entered as a percentage; the monthly rate r is APR ÷ 1,200. n is the number of monthly payments, calculated as loan term in years × 12. M is the monthly payment in dollars, rounded to cents before totals are calculated. T is the total paid over the stated term, and I is the portion of that total above the principal. This calculator uses a positive APR; it does not model a zero-interest loan.

Worked Example

Using the calculator’s default inputs: P = $20,000, APR = 8%, and term = 5 years.

1. Convert the APR to a monthly rate: r = 8 ÷ 1,200 = 0.0066667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Calculate the payment: M = round[$20,000 × 0.0066667 ÷ (1 − (1.0066667)⁻⁶⁰), 2] = $405.53 per month.
4. Multiply the rounded payment by the number of payments: T = $405.53 × 60 = $24,331.80.
5. Subtract the principal: I = $24,331.80 − $20,000 = $4,331.80 in total interest.

The payment is rounded to cents before the total is computed, so the total reflects 60 payments of $405.53. A lender’s actual payment schedule can differ because of its rounding, payment dates, fees, or contract terms.

Assumptions

• The APR is fixed throughout the term.
• There are equal monthly payments, with the first payment one month after the loan begins.
• Interest accrues monthly using APR ÷ 12; the equation treats the quoted APR as a nominal annual rate.
• Fees, taxes, insurance, PMI, escrow, late charges, and other costs are not included.

What “Total Cost” Includes

The phrase “total cost” can refer to more than one number. In a basic amortizing-loan calculation, total of payments means all scheduled principal and interest payments added together. Total interest isolates the financing cost above the amount borrowed. Neither figure automatically includes charges paid separately or added to the balance.

For the example, the borrower receives $20,000 and is scheduled to pay $24,331.80 in installments. The difference, $4,331.80, is the estimated interest under the assumptions above. If a loan has an origination charge, for example, the overall cash cost could be higher. The charge cannot be incorporated accurately without its amount and the way it is collected.

Always distinguish a loan’s principal from its total of payments. Principal is what is borrowed; it is not the total amount repaid. Also distinguish interest from fees: a fee may be part of the cost of borrowing but is not necessarily included in the interest figure shown here.

When to Use the Equation

This equation is useful for understanding the arithmetic of a conventional fixed-rate loan when the principal, APR, and term are known. It can help explain why a longer term generally produces more scheduled payments, and why changing the APR changes the payment and interest total. It is an estimate for comparing stated loan terms, not a complete accounting of every expense or a prediction of approval.

Use figures that match the lender’s offer: the amount actually financed, the stated APR, and the repayment term. If a fee is financed, it may be part of the principal used for the payment calculation. If the APR or balance can change, or payments are not equal and monthly, this fixed-payment equation may not describe the contract. Obtain the actual rate, fees, and payment schedule from the lender rather than assuming an example figure applies.

Common Errors and Limits

• Using APR as the monthly rate: An APR of 8% is entered as 8, then divided by 1,200 to get a monthly decimal rate. Do not enter 0.08 as though it were 8% in this calculator.
• Confusing term units: The input is years, while the formula needs monthly payments. The calculator multiplies years by 12.
• Rounding too early: Rounding the monthly payment to cents is part of this calculator’s stated method. Small differences may appear if a lender uses a different rounding procedure or adjusts a final payment.
• Assuming every borrowing cost is included: The equation does not add fees, insurance, taxes, or optional products unless they are included in the loan amount or entered separately.

The formula is designed for a fixed rate and a regular amortizing schedule, where each payment covers accrued interest and reduces the outstanding principal. It is not a payoff quote: an early payoff amount depends on the balance and date, and may also involve contract-specific charges. For variable rates, irregular payment dates, deferred payments, or a changing payment, use the lender’s schedule or a model that explicitly represents those terms.

Frequently Asked Questions

What is the total cost equation?
For equal monthly payments, total of payments = monthly payment × number of payments. To find total interest, subtract the amount borrowed from that total.

Is total cost the same as total interest?
No. Total of payments includes repayment of principal as well as interest. Total interest is the amount paid above principal under the calculation’s assumptions.

Does total cost include loan fees?
Not in this calculator. Fees are excluded unless they are included in the principal entered, and even then the result does not identify them as separate fees.

Why can my lender’s total differ?
The lender may use different rounding, payment dates, fees, or contract terms. A variable rate or a financed charge can also change the actual payment schedule.

Can I use this equation for a zero-interest loan?
This calculator requires a positive APR. For a genuinely zero-interest loan with equal monthly payments, the basic payment is principal divided by the number of payments, but other contract costs may still apply.

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

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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