Rate and Term Loan Calculator: Payment and Interest

A rate-and-term loan calculator estimates the monthly payment and total interest for a loan when you enter its amount, annual percentage rate (APR), and repayment term. It assumes equal monthly payments at a fixed rate and does not model fees or other loan costs.

Formula

The calculator uses the standard fixed-rate, fully amortizing loan payment formula. It first calculates the monthly payment, rounds that payment to the nearest cent, and then estimates total interest from the rounded payment:

• Monthly payment: M = round[P × r ÷ (1 − (1 + r)⁻ⁿ), 2]
• Total interest: I = M × n − P
• Monthly rate: r = APR ÷ 1,200
• Number of payments: n = years × 12

P is the starting loan principal in dollars; APR is the annual percentage rate entered as a percent; r is the monthly rate as a decimal; n is the number of monthly payments; M is the monthly payment in dollars; and I is estimated interest in dollars. For example, an APR of 8% becomes 0.08 ÷ 12, or about 0.006667 per month. The expression uses APR as a nominal annual rate divided by 12, not an effective annual yield.

Worked Example

Using the calculator’s default values—$20,000 principal, 8% APR, and a five-year term:

1. Convert the rate to a monthly decimal: r = 8 ÷ 1,200 = 0.0066667.
2. Convert the term to payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = round[20,000 × 0.0066667 ÷ (1 − (1.0066667)⁻⁶⁰), 2] = $405.53 per month.
4. Calculate interest using the rounded payment: I = $405.53 × 60 − $20,000 = $4,331.80.

The corresponding total of scheduled payments is $24,331.80: 60 payments of $405.53. The final payment on an actual loan may differ slightly because lenders can calculate interest and round balances according to their own schedules.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and begin one month after the loan is issued.
• Interest is modeled monthly at APR divided by 12.
• Fees, taxes, insurance, mortgage insurance, escrow, late charges, and payment-date effects are not included.

What a Rate-and-Term Loan Means

“Rate and term” can describe changing a loan’s interest rate, repayment length, or both while keeping the borrowing purpose and underlying debt broadly the same. The phrase is often used when discussing refinancing: a borrower replaces an existing loan with another, and the new contract has a different rate or term. It is also used more generally to distinguish those changes from borrowing additional money against an asset.

The calculator does not determine whether a transaction qualifies as a rate-and-term refinance, or whether a lender will offer particular terms. Those definitions and eligibility decisions depend on the specific contract and lender. Here, “rate” means the APR entered for the modeled loan, and “term” means the number of years until its scheduled final payment.

How to Read the Results

The monthly payment is the modeled amount due each month for principal and interest. Early in an amortizing loan, a larger share of each payment generally goes toward interest; over time, the interest portion declines as the balance is paid down. The total-interest output estimates the interest paid over all scheduled payments if the assumptions hold and payments are made as modeled.

These figures are not a quote or a complete borrowing cost. APR may reflect certain costs in a lender’s disclosure, while this calculator applies the entered APR as the rate in a simplified monthly-payment equation. It does not separately add closing costs, origination charges, or other fees. Get the actual rate, fees, payment schedule, and total cost from the lender’s written disclosure.

Comparing Rates and Terms

Changing the rate or term changes the payment and total interest in different ways. With the same principal and term, a higher entered rate increases the modeled payment and interest. With the same principal and rate, a longer term generally reduces each scheduled payment but increases the number of payments over which interest accrues. A shorter term usually has the opposite pattern.

For a neutral comparison, change one input at a time and keep the principal constant. Then compare both the monthly payment and total interest—not just the payment. For example, a lower monthly figure from a longer term does not mean the loan costs less overall. A real comparison should also account for fees, timing, and any differences in how the lender calculates APR and payments.

Common Limitations and Mistakes

• Entering 8 instead of 0.08: Enter APR as a percentage, such as 8 for 8%, not as a decimal. The formula performs the conversion.
• Mixing years and months: The term field is in years; the calculator multiplies it by 12 to obtain monthly payments.
• Treating the result as a payoff quote: A payoff amount can include accrued interest, fees, or other contract-specific items that this calculation omits.
• Ignoring payment rounding: The monthly amount is rounded to cents, so multiplying that displayed payment by the number of months is the calculator’s basis for total interest. A lender’s final payment can vary due to its precise schedule.
• Assuming a variable rate stays unchanged: The calculation assumes a fixed APR. It cannot forecast future payment changes on a variable-rate loan.

Use the calculation as an estimate of standard loan arithmetic, not as a prediction of approval or an instruction to borrow. A lender’s contract may use different payment timing, fees, or rounding, and those details can change the figures.

Frequently Asked Questions

What is a rate-and-term loan?
A rate-and-term loan generally refers to changing a loan’s interest rate, repayment period, or both without focusing on taking additional cash out. The exact meaning can depend on the lender and transaction.

Does a longer loan term lower the payment?
For the same principal and fixed rate, spreading repayment over more monthly payments generally lowers the scheduled payment. It can increase total interest because the balance is outstanding for longer.

Is APR the same as the interest rate?
Not necessarily. APR is a disclosure measure that may account for certain loan costs, while the note rate is the rate used to accrue interest under the contract. This calculator treats the entered APR as its modeled rate and does not separately model fees.

Does this calculator include fees or closing costs?
No. It estimates principal-and-interest payments and interest only. Ask the lender for a written breakdown of fees and other amounts that may be due.

Why might my lender’s payment be different?
The lender may use a different disclosed rate, payment date, fee treatment, rounding method, or final-payment adjustment. Compare the calculator inputs with the lender’s disclosure and payment schedule.

The result is an estimate, and 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 int | Total interest | $ | pmt * yrs * 12 - p | 2