Amortization

Amortization is the schedule that retires a loan in level payments. The lender sets one payment that, made every month for the term, covers each month's interest on the remaining balance and repays the whole principal by the last month; the schedule lists, for every month, how much of the payment is interest, how much is principal, and what is still owed. Because the interest is charged on the remaining balance, early payments are mostly interest and late payments mostly principal, though the payment itself never changes, which is why a loan's balance falls slowly at first and quickly at the end.

In a sentence

• "The amortization schedule splits the first $395.08 payment into $115 of interest and $280.08 of principal, and the last one into $2.26 and $392.92."
• "Ten years into a thirty-year mortgage's amortization, about $254,000 of a $300,000 loan is still owed."
• "A credit card has no amortization schedule; the balance is whatever you carried, and the payoff date is whatever your payments make it."

How it works

1. The payment is set from the amount, the rate and the term with one formula, so the last payment leaves exactly zero.
2. Each month, the interest is the monthly rate times the balance still owed. In the first month that is the whole loan.
3. The rest of the payment is principal, and it comes off the balance.
4. The next month's interest is charged on the smaller balance, so it is a little lower, and the principal share a little higher, than the month before.
5. The schedule ends when the balance reaches zero, on the last scheduled payment, or earlier for a loan paid ahead.

Payment = P × r ÷ (1 − (1 + r)^−n), where P is the amount borrowed, r the annual rate ÷ 12, and n the number of monthly payments

Interest for the month = balance × r; principal for the month = payment − interest

A lender rounds the payment to the cent and adjusts the final payment to whatever is left. Mortgages, car, student and personal loans amortize; interest-only loans and revolving balances do not.

An example

A $20,000 car loan at 6.9% over sixty months, the example's assumptions, has a payment of $395.08. The first payment is $115.00 of interest and $280.08 of principal; the sixtieth is $2.26 and $392.92, a final payment of $395.18. The schedule by year:

The first year pays $1,272 of interest and the last $173, on the same twelve payments. The same arithmetic on a $300,000 mortgage at 6.5% over thirty years gives a payment of about $1,896, of which $1,625 is interest in the first month and $271 principal; after ten years, about $254,000 is still owed.

Why it matters

The schedule is the true price of a term and the reason an extra payment is worth more early than late. A longer term lowers the payment by retiring less principal each month, and the interest on the slower-falling balance adds up: the same $20,000 at 6.9% over 72 months is $340.02 a month instead of $395.08, and $4,481.47 of interest instead of $3,704.90. An extra $100 a month on the sixty-month loan, all of it principal, ends it in 47 months and saves $879.68. The mistake the schedule prevents is assuming the loan is half paid at the halfway point: at month 30 of 60 the car loan still owes $10,857.96, and at year 10 of 30 the mortgage still owes about 85% of what was borrowed; a loan refinanced then starts a new schedule at the interest-heavy end.

Amortization versus interest-only and revolving debt

An amortizing loan has a fixed payment and a known end: every payment retires some principal, and the balance reaches zero on the last scheduled month. An interest-only loan's payment covers the interest and nothing else, so the principal is untouched until a lump sum or a later amortizing phase. A revolving balance, a credit card or a home equity line in its draw period, has no schedule at all: the balance is whatever has been charged and carried, the minimum payment is recomputed each month, and there is no end date unless the borrower fixes the payment, which is what a payoff calculator does.

Common questions

Is amortization the same as depreciation? No. Depreciation is an asset losing value over time, a car worth less each year. Amortization is a loan being repaid on a schedule. In accounting the word has a third use, spreading the cost of an intangible asset over its useful life, which shares the shape but not the subject.

Why does the balance fall so slowly at first? Because the interest is charged on the whole remaining balance, and at the start the balance is the whole loan. A fixed payment covers that interest first, so the principal share is smallest in the first month and grows only as the balance falls.

Does an extra payment change the schedule? Yes. An extra payment applied to principal lowers the balance, so every later interest charge is smaller and the loan ends earlier; the regular payment stays the same unless the lender recasts the loan. Check that the extra goes to principal rather than to the next scheduled payment.

What is negative amortization? A payment smaller than the month's interest. The unpaid interest is added to the balance, so the loan grows instead of shrinking. It happens where a loan allows a payment below the interest, such as some adjustable-rate mortgages with a payment cap, and on a student loan whose interest accrues unpaid during a pause.

Do credit cards amortize? Not on their own. A card has no term and no fixed payment, so its balance has no schedule; the minimum shrinks with the balance and the payoff stretches. A fixed payment you set yourself amortizes the balance like a loan, and the payoff calculator sizes that payment for the date you want.

Go deeper

• The Loan calculator turns an amount, a term and a rate into the monthly payment, the total interest, and a year-by-year schedule, and shows how much sooner the loan ends with a little extra each month.
• The Mortgage calculator estimates the full monthly payment on a home, principal and interest plus property tax, insurance, HOA dues and PMI, with the total interest over the life of the loan.
• How paying off debt raises your net worth follows the principal portion of each payment onto the other side of the ledger.

Where it shows up in Zypper

Zypper does not draw the schedule, but it shows the schedule's result. Loans, including mortgages and auto, student and personal loans, connect and contribute their balances to the liability side of net worth, which is computed from every account and charted over time, so a balance falling by each payment's principal is a line rather than a column in a table; a loan that cannot be connected is added as a manual account whose balance you set to the remaining principal and update when the statement arrives. See Net worth tracking and Manual accounts for the details, or get started with Zypper to see the balance fall on its schedule.