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Loan

How To Calculate Loan Payment

An amortizing loan keeps the payment fixed while the split between interest and principal changes every month. The formula that produces that payment — and the amortization behind it — explains why shortening the term saves so much.

Quick Answer

M = P x r(1 + r)^n / ((1 + r)^n - 1)

M
Fixed payment per period
P
Loan principal — the amount borrowed
r
Interest rate per period as a decimal (annual rate / 12)
n
Total number of payments

Multiply the principal by the periodic interest rate and by one plus that rate raised to the number of payments, then divide by that same factor minus one. The result is the fixed payment that retires the balance exactly at the end of the term.

What Is Loan Payment?

An amortizing loan is designed so the same amount leaves your account every month, but what that amount pays for shifts continuously. Early payments are mostly interest because the balance is at its largest; later payments are mostly principal because there is less left to charge interest on. The payment itself never changes.

To see why, follow the mechanics for one month. Interest due equals the outstanding balance times the monthly rate. Whatever portion of the fixed payment exceeds that interest goes to principal, shrinking the balance. Next month interest is computed on the smaller balance, so a larger share of the identical payment retires principal. This self-correcting loop is what guarantees the balance hits exactly zero on the final payment.

The formula is derived by setting the loan's present value equal to the present value of the payment stream, then solving for the payment. Every payment is discounted back to today, they sum to the principal, and algebra produces the closed form above. Nothing about the derivation depends on the loan type, which is why the identical expression governs mortgages, auto loans and student loans alike.

Term length is the variable that surprises people most. On $300,000 at 6.5%, a thirty-year mortgage costs $1,896.20 a month while a fifteen-year mortgage costs $2,613.32 — only 37.8% more per month. But total interest paid drops from about $382,633 to about $170,398, a saving of more than $212,000. Doubling the term does not halve the payment; it barely moves it, while more than doubling the total cost.

The payment formula covers principal and interest only. Real monthly housing costs also include property taxes, homeowners insurance, mortgage insurance and association dues. Those are commonly collected with the payment and can add twenty to thirty percent on top of the computed figure, so never compare a computed P&I against a quoted monthly housing budget without checking what the quote includes.

What the formula does not see is anything that changes mid-stream: extra principal payments, a refinance, an adjustable rate resetting, or an escrow shortage. Each of those re-amortizes what remains. Handle them by recomputing with the outstanding balance as the new principal and the remaining payments as the new n.

Every amortizing loan has a crossover point, and on a thirty-year mortgage it arrives far later than most borrowers expect. Because interest is computed on the outstanding balance, the first payment of $1,896.20 sends $1,625.00 to interest and only $271.20 to principal — 85.70 percent of it is interest. The payment does not split evenly into half principal until payment 233 of 360, in the twentieth year. The fifteen-year loan reaches the same crossover at payment 53 of 180, in year five. That gap is the real reason shorter terms save so much: not a better rate, but a balance that starts falling toward zero immediately instead of drifting for two decades.

Formula

M = P x r(1 + r)^n / ((1 + r)^n - 1)

Standard amortization. Produces the level payment that retires principal exactly over n periods at a periodic rate r.

SymbolMeaning
PPrincipal borrowed
rInterest rate per payment period
nTotal number of payments
MPayment per period

B = P(1 + r)^k - M x (((1 + r)^k - 1) / r)

Grow the original principal forward k periods, then subtract the accumulated value of the payments made so far. This is how the interest/principal split is computed month by month.

SymbolMeaning
kNumber of payments already made

How To Calculate Loan Payment

  1. 1

    Determine the amount actually financed

    Start from the price, subtract the down payment, and add any fees being rolled into the loan. Financing $300,000 on a $375,000 home means P = 300,000, not 375,000.

  2. 2

    Convert the annual rate to a periodic rate

    Divide by 12 for monthly payments: 6.5% becomes 0.065 / 12 = 0.0054167. Using the annual rate here would charge twelve years of interest in one month.

  3. 3

    Count the total number of payments

    Years times twelve for a monthly schedule. Thirty years gives n = 360, fifteen years gives n = 180. Biweekly and weekly schedules use different counts and a correspondingly different rate.

  4. 4

    Evaluate the payment factor

    Compute (1 + r)^n first. For r = 0.0054167 and n = 360 that is about 6.991798. The rest is substitution into the fraction.

  5. 5

    Solve for M and check it against total cost

    M = $300,000 x 0.0054167 x 6.991798 / (6.991798 - 1) = $1,896.20. Multiply by 360 to get total paid, then subtract principal for total interest — the number that actually tells you what the loan costs.

Examples

Example 1: 30-year mortgage — $300,000 at 6.5%

P
$300,000
Annual rate
6.5%
Term
30 years
n
360 months
StepCalculationResult
Monthly rate0.065 ÷ 120.0054167
Compound term(1 + 0.0054167)^3606.991798
Numerator part$300,000 x 0.0054167 x 6.991798$11,361.67
Payment$11,361.54 ÷ 5.991798$1,896.20
Total paid over 360 months$1,896.20 x 360$682,633.47
Total interest$682,633.47 - $300,000$382,633.47

Result: Monthly payment $1,896.20; total interest $382,633.47

Example 2: 15-year mortgage — same $300,000 at 6.5%

P
$300,000
Annual rate
6.5%
Term
15 years
n
180 months
StepCalculationResult
Compound term(1 + 0.0054167)^1802.644201
Numerator part$300,000 x 0.0054167 x 2.644201$4,296.83
Payment$4,296.83 ÷ 1.644201$2,613.32
Total paid over 180 months$2,613.32 x 180$470,397.98
Total interest$470,397.98 - $300,000$170,397.98

Result: Monthly payment $2,613.32; total interest $170,397.98 — saving $212,235.49

Calculator

Monthly payment

$1,896.20

Total of all payments
$682,633.47
Total interest
$382,633.47

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

Prefer a full-width tool? Open the Loan Payment calculator page.

Common Mistakes

  • Dividing by the wrong period count in the rate

    Using an annual rate with monthly payments multiplies the interest by roughly twelve. Always convert both together: monthly rate with monthly n, annual rate with annual n.

  • Assuming the payment covers taxes and insurance

    This formula produces principal and interest only. Escrowed property taxes, homeowners insurance and mortgage insurance commonly add twenty to thirty percent, so a computed figure is never the full monthly housing cost.

  • Comparing lenders on monthly payment alone

    A longer term always produces a smaller payment and always costs more overall. Compare total interest — or the total of payments over the full term — rather than the monthly number that fits a budget more comfortably.

  • Ignoring fees rolled into the financed principal

    Origination and Points financed rather than paid upfront raise P, increasing both the payment and the total interest. Compare offers on the financed amount and the APR, not on the headline rate alone.

  • Assuming the quoted rate is the effective cost

    With monthly compounding the effective annual cost exceeds the nominal rate. APR is designed to expose this by including certain fees, which is why it is legally required to be disclosed alongside the nominal rate.

FAQ

Why does so much of my early payment go to interest?

Interest is charged on the outstanding balance, which is largest at the start. Early payments therefore cover mostly interest and retire little principal. As the balance falls, the interest portion shrinks and progressively more of the same payment reduces principal.

How much does shortening the term actually save?

A great deal. On $300,000 at 6.5%, moving from thirty years to fifteen raises the payment by about 37.8% but cuts total interest from roughly $382,633 to $170,398 — a saving over $212,000.

What happens if I make extra principal payments?

The balance drops faster, so future interest is charged on a smaller amount and the loan ends early. Recompute using the current balance as P and the remaining payment count as n to see the new payoff date.

Does this formula work for car loans and student loans?

Yes. Any fully amortizing loan with a fixed rate uses the identical expression. Supply the financed amount, the monthly rate and the number of scheduled payments, and the arithmetic is unchanged.

What is the difference between the interest rate and the APR?

The interest rate drives the payment; the APR includes that rate plus certain fees expressed as an annualized cost. Because it spreads fees across the whole loan, APR is the better figure for comparing two offers side by side.

References

  1. [1]Consumer Financial Protection Bureau, Truth in Lending Act — Regulation Z, Closed-End Credit — https://www.consumerfinance.gov/rules-policy/regulations/1026/
  2. [2]Federal Reserve Board, Consumer Handbook on Adjustable Rate Mortgages and Loan Disclosures — https://www.federalreserve.gov/pubs/arm/
  3. [3]OpenStax, Principles of Finance — Amortized Loans, 2024 — https://openstax.org/details/books/principles-finance