Loan Calculator

This calculator finds the monthly payment of a loan, and how much it costs in total, for a fixed-rate loan repaid in equal monthly payments, as most mortgages, car loans and personal loans are. Enter the amount borrowed, the yearly interest rate and the term in years or months.

The formula

Monthly payment = P * r / (1 - (1 + r)^(-n))

with P the amount borrowed, r the monthly interest rate and n the number of monthly payments. The calculator works out the last two in the background:

• Monthly rate: the yearly rate divided by 12, as a decimal. 6% a year is 0.06 / 12 = 0.005.
• Number of payments: the term in months. 5 years is 60.

The total paid is the monthly payment times the number of payments, and the interest is the total minus the amount borrowed.

Example

$20,000 at 5% a year over 5 years:

1. Monthly payment: with r = 0.05 / 12 and n = 60.

   377.42

2. Total paid:

   377.42 * 60 = 22,645.20

3. Interest:

   22,645.20 - 20,000 = 2,645.20

The same loan over 7 years lowers the payment to 282.68, but raises the interest to 3,745.12.

Frequently asked questions

How does each payment split between interest and principal?

Each month, the interest is the monthly rate times what is still owed, and the rest of the payment reduces the loan. Early payments are mostly interest; later ones mostly principal. In the example, the first month's interest is 20,000 * 0.05 / 12 = 83.33, and the other 294.09 repays the loan.

Does this include fees or insurance?

No. It covers the loan's interest only. Arrangement fees, insurance and taxes add to the real cost, which the APR the lender quotes includes.