Amortization Calculator

What each input means

• Loan amount: the principal you borrow, or the balance you still owe.
• Annual interest rate: the nominal annual rate. The rate per period is the annual rate divided by the number of payments per year.
• Loan term: the length of the loan in years. The number of payments is years × payments per year.
• Payment frequency: how often you pay. Semimonthly means 24 payments a year (twice a month); quarterly means 4.

How the schedule is built

i = Annual rate ÷ payments per year      n = years × payments per year
Payment = P × i ÷ (1 − (1 + i)^−n)
Interest_k = Balance_(k−1) × i
Principal_k = Payment − Interest_k
Balance_k = Balance_(k−1) − Principal_k

Because interest is charged on a shrinking balance, each payment contains a little less interest and a little more principal than the one before. The final balance is zero.

How to read the schedule

• Early payments: most of the money goes to interest, so the balance falls slowly.
• Crossover payment: the first period in which principal exceeds interest. On long loans it comes late; on a 30-year mortgage at 6%, it's payment 223.
• Yearly summary: total payments, interest and principal for each year plus the year-end balance, handy for budgeting or for your tax records.
• Interest share: the percentage of everything you pay that goes to interest.

If you plan to make extra payments, the schedule shows why sooner is better: early on, every extra dollar of principal avoids the most interest.

Comparing payment frequencies

With the same annual rate and term, paying more often lowers total interest slightly because the balance drops sooner.

Semimonthly (24 payments a year) is not the same as biweekly (every two weeks, 26 payments a year). Biweekly plans make the equivalent of one extra monthly payment each year, which shortens the loan.

What it's useful for

• Checking the payment schedule your lender gave you and spotting differences.
• Finding out how much you owe in a given month, for example before selling or refinancing.
• Comparing monthly with semimonthly or quarterly payments at the same annual rate.
• Planning how much interest you'll pay each year.

Example

A $10,000 loan at 12% for 3 years with monthly payments: 36 payments of $332.14. The first payment is $100.00 interest and $232.14 principal, leaving a balance of $9,767.86. By the end of year one you owe $7,055.84, and over the whole loan you pay $1,957.15 in interest.

1. i = 12% ÷ 12 = 1% per month; n = 36
2. Payment = 10,000 × 0.01 ÷ (1 − 1.01^−36) = $332.14
3. Payment 1: interest $100.00; principal $232.14; balance $9,767.86
4. Payment 2: interest $97.68; principal $234.46; balance $9,533.39
5. Total interest = $332.14 × 36 − $10,000 ≈ $1,957.15

Common mistakes

• Dividing the annual rate by 12 when payments aren't monthly. With quarterly payments, divide by 4.
• Assuming each payment reduces the debt by its full amount. Early on, most of it is interest.
• Comparing with your lender's statement without accounting for escrow, insurance or fees added to each payment.
• Confusing semimonthly payments (24 a year) with biweekly payments (26 a year).