Loan Calculator: Monthly Payment & Total Interest

A loan calculator works out the fixed payment on a loan from three inputs: the amount borrowed, the annual interest rate, and the length of the loan. It also shows the number of payments, the total interest, and the total amount paid over the life of the loan.

How the loan calculator works

The calculator models a fixed-rate amortizing loan. "Amortizing" means the debt is paid off gradually with equal payments. Each payment first covers the interest that has built up on the remaining balance. The rest of the payment reduces the balance itself. The payment is sized so the balance reaches exactly zero on the final payment.

The tool takes four inputs:

• Loan amount: the principal, from $1 to $100,000,000.
• Annual interest rate (APR): from 0% to 100%.
• Loan term: a whole number of years, from 1 to 50.
• Repayment frequency: monthly (12 payments a year), bi-weekly (26), or weekly (52).

From these it reports the payment per period, the number of payments, the total interest paid, and the total paid. A bar below the results shows what share of the total goes to principal and what share goes to interest.

Loan payment formula

The calculator first converts the annual rate into a rate per payment period:

$i = \frac{r}{100 \times p}$

where i is the rate per period, r the annual rate as a percentage and p the number of payments per year. A 6% annual rate with monthly payments gives i = 6 / 100 / 12 = 0.005, or 0.5% per month.

The number of payments is the term in years times the payments per year:

$n = y \times p$

where n is the number of payments and y the term in years.

The payment is then:

$M = \frac{P \times i \times (1 + i)^n}{(1 + i)^n - 1}$

where M is the payment per period and P the loan amount. When the rate is 0%, the formula would divide zero by zero, so the calculator instead splits the principal evenly:

$M = \frac{P}{n}$

The two totals follow directly from the payment:

$T = M \times n$

$I = M \times n - P$

where T is the total paid and I the total interest.

Total interest is everything paid above the amount borrowed. This calculator counts only interest. It does not include origination fees, insurance, or taxes.

Worked example

A borrower takes a $10,000 loan at 6% annual interest for 5 years, repaid monthly.

1. Period rate: i = 6 / 100 / 12 = 0.005.
2. Number of payments: n = 5 × 12 = 60.
3. Growth factor: (1.005)^60 ≈ 1.34885.
4. Payment: M = 10,000 × 0.005 × 1.34885 / 0.34885 ≈ $193.33 per month.
5. Total paid: about $11,599.68.
6. Total interest: about $1,599.68.

The breakdown bar for this loan shows 86.2% principal and 13.8% interest.

A second example: $20,000 at 7.5% for 4 years, monthly. The period rate is 0.00625 and there are 48 payments. The payment is $483.58, the total paid is $23,211.75, and the total interest is $3,211.75.

At 0% the math is simpler. A $9,000 loan over 3 years, monthly, costs 9,000 / 36 = $250.00 per month, with $0 interest.

Monthly, bi-weekly, and weekly payments

Paying more often lowers the total interest slightly, because the balance shrinks a little sooner. For the $10,000 loan at 6% over 5 years:

In this calculator, bi-weekly means every two weeks: 26 payments a year, not 24. Some lenders instead offer "semi-monthly" plans with two payments a month (24 a year). Those are a different schedule and give slightly different numbers.

The savings from paying more often are small here because each schedule still runs the full 5 years. Larger savings come from accelerated plans that keep the monthly payment amount but split it into halves every two weeks, which this calculator does not model.

Conventions the calculator uses

Loan math has a few points where tools can reasonably differ. This calculator resolves them as follows.

The rate is a nominal annual rate. The annual percentage is divided by the number of payments per year to get the period rate. This is the standard APR convention used for most consumer loans in North America. It is not an effective annual rate, so 6% compounded monthly costs slightly more than 6% over a year: (1.005)^12 − 1 ≈ 6.17%.

Totals come from the unrounded payment. The tool computes the exact payment, multiplies by the number of payments, and only rounds the results for display. In the first example the exact payment is $193.3280…, so the total paid shows $11,599.68. Multiplying the rounded payment instead gives 193.33 × 60 = $11,599.80, which is 12 cents higher. Real lenders round each payment to the cent and adjust the final payment, so a statement from a bank can differ from the tool by a few cents.

Total interest is total paid minus principal. Nothing else is added or subtracted, since the tool models no fees.

Limits

The calculator accepts loan amounts from $1 to $100,000,000, rates from 0% to 100%, and whole-year terms from 1 to 50 years. Values outside these ranges, or a term with a fraction of a year, produce an error message instead of a result.

Frequently asked questions

Why is the bi-weekly total interest lower than the monthly total?

With 26 smaller payments a year, part of the balance is repaid earlier in each month, so slightly less interest accrues. Over the same term the difference is modest: about $13 on a $10,000 loan at 6% over 5 years.

Does the calculator include fees or taxes?

No. It computes interest only. Origination fees, late fees, insurance, and taxes are not part of the result. A lender's APR disclosure may fold some fees into the quoted rate, so the quoted APR can be higher than the note rate.

Why doesn't the payment times the number of payments exactly match the total paid?

The tool multiplies the exact, unrounded payment by the number of payments and rounds at the end. Multiplying the rounded payment gives a slightly different number. The gap is at most a few cents per payment.

Can the interest rate be 0%?

Yes. At 0% the payment is simply the loan amount divided by the number of payments, and the total interest is $0. Promotional financing sometimes works this way.

What kinds of loans does this fit?

Any fixed-rate loan repaid in equal installments: personal loans, auto loans, student loans with fixed rates, and standard mortgages. It does not fit variable-rate loans, interest-only loans, or credit card balances, where the payment or rate changes over time.