CalculateY CalculateY

Loan Interest Calculator

The standard amortization formula, M = P[r(1+r)^n]/[(1+r)^n-1], calculates the fixed monthly payment for a loan based on the principal, interest rate, and term. A $20,000 loan at 7% for 5 years has an estimated monthly payment of approximately $396 and approximately $3,761 in total interest. Enter your loan details below to see estimated costs, and optionally add extra monthly payments to see potential interest savings.

Quick Answer

A $20,000 loan at 7% annual interest for 5 years has an estimated monthly payment of approximately $396 and approximately $3,761 in total interest over the life of the loan.

Common Examples

Input Result
$10,000 at 5% for 3 years Estimated $300/month, $790 total interest
$20,000 at 7% for 5 years Estimated $396/month, $3,761 total interest
$50,000 at 8% for 10 years Estimated $607/month, $22,793 total interest
$30,000 at 6% for 7 years, $100 extra/month Estimated $438/month, payoff in ~57 months

How It Works

This calculator uses the standard amortization formula to estimate fixed monthly payments for a loan:

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

Where:

  • M = estimated monthly payment
  • P = loan principal (the amount borrowed)
  • r = monthly interest rate (annual rate divided by 12, expressed as a decimal)
  • n = total number of monthly payments (loan term in years multiplied by 12)

The estimated total paid over the life of the loan is M x n. The estimated total interest is the total paid minus the original principal.

Extra Payments

When you make extra payments each month, the additional amount goes directly toward reducing the principal balance. This has two effects: it shortens the payoff period and reduces the total interest paid. The calculator simulates month-by-month amortization with the extra payment applied to show the estimated savings compared to the standard payment schedule.

For a 0% interest rate, the estimated monthly payment is simply the principal divided by the number of months.

Worked Example

For a $20,000 loan at 7% annual interest for 5 years (60 months): Monthly rate r = 0.07/12 = 0.005833. Factor = (1.005833)^60 = 1.4176. M = 20000 x [0.005833 x 1.4176] / [1.4176 - 1] = 20000 x 0.008270 / 0.4176 ≈ $396.02 per month. Estimated total paid = $396.02 x 60 = $23,761. Estimated total interest = $23,761 - $20,000 = $3,761. With an extra $100/month payment, the loan would pay off in approximately 47 months instead of 60, saving an estimated $1,103 in interest.

Related Calculators

Mortgage Calculator

Estimate your monthly mortgage payment, total interest, and total cost based on loan amount, interest rate, and term.

Compound Interest Calculator

Estimate how your investments may grow over time with compound interest and regular contributions.

Car Loan Calculator

Estimate your monthly car payment, total interest, and total cost based on loan amount, rate, and term.

Frequently Asked Questions

How is the monthly loan payment estimated?
The calculator uses the standard amortization formula, which computes the fixed monthly payment needed to fully repay a loan over a specified term at a given interest rate. Each payment covers that month's interest charge plus a portion of the principal. Early payments are mostly interest, while later payments are mostly principal.
How do extra payments reduce total interest?
Extra payments go directly toward reducing the outstanding principal balance. Since interest is calculated on the remaining balance each month, a lower balance means less interest accrues. This creates a compounding savings effect: each extra payment reduces the balance, which reduces future interest charges, which means more of each subsequent payment goes toward principal.
Does this calculator include taxes or fees?
No. This calculator estimates loan interest and payments only. Origination fees, closing costs, insurance, and taxes are not included. The actual cost of a loan may be higher than the estimated interest shown here.
What types of loans does this work for?
This calculator works for any fixed-rate amortizing loan, including personal loans, auto loans, student loans, and fixed-rate mortgages. It does not account for variable rates, interest-only periods, or balloon payments.
What is the difference between interest rate and APR?
The interest rate is the percentage charged on the outstanding loan balance. The annual percentage rate (APR) includes the interest rate plus certain fees and costs, providing a more complete picture of the total borrowing cost. This calculator uses the interest rate, not APR.