Amortization

An amortizing loan is built so that one level payment repays it exactly by the end of the term. Each month the lender charges interest on the balance still owed, at one-twelfth of the annual rate. Whatever is left of your payment after interest reduces the principal. The next month’s interest is figured on that slightly smaller balance, so a little more of the same payment goes to principal each time.

That is why the early years feel slow. On a 30-year Mortgage at 6.95%, the first payment is almost 88% interest, and after 10 years of payments you have repaid only about 14% of what you borrowed. The pattern flips late in the loan, when nearly the whole payment is principal. The rate hasn’t changed; you simply owe less, so less interest accrues.

Unlike compound interest on savings, loan interest is paid off every month, so it doesn’t build on itself unless a payment falls short. Car loans, student loans, personal loans and fixed-rate mortgages amortize this way. Credit cards are revolving debt with minimum payments that shift with the balance, so they have no fixed schedule unless you set one yourself.

You need three numbers: the amount borrowed, the annual interest rate and the number of monthly payments. Put them into the payment formula below to get the level payment. Then build the schedule one row at a time, following the steps in the list, until the balance reaches zero.

The table further down condenses the 360 rows of a $400,000, 30-year loan at 6.95% into seven snapshots. Each full year’s interest and principal add up to the same 12 payments of $2,647.79, about $31,774; only the split between them changes. Spreadsheet functions such as PMT, IPMT and PPMT do exactly this arithmetic, which makes it easy to test a different rate, term or extra payment.

Because interest is charged on the balance, every dollar of extra principal stops accruing interest for the rest of the loan. On the $400,000 example, adding $200 a month pays the loan off in 24 years and 3 months instead of 30, and cuts total interest from about $553,200 to about $428,100, a saving of roughly $125,100. Paying one-twelfth of a payment extra each month, the same as one extra payment a year and roughly what a biweekly plan of 26 half-payments achieves, finishes in about 23 years and 10 months.

On a standard fixed-rate loan, extra payments don’t lower the required monthly payment; they end the loan sooner. Check first for a prepayment penalty. Federal rules allow one only on a Qualified Mortgage whose APR can’t rise after closing and that isn’t a higher-priced loan. The penalty can’t exceed 2% of the amount prepaid in the first two years or 1% in the third year, can’t apply after three years, and the lender must also offer a loan without one. The CFPB notes that penalties normally target paying off the whole loan, not extra principal in small amounts.

Prepaying isn’t automatically the best use of spare cash. It earns a guaranteed return equal to the loan’s rate, less any tax saved on the interest, but the money is no longer liquid. An emergency fund, an employer 401(k) match and higher-rate balances, which come first under the debt avalanche method, usually rank ahead of it.

Not every loan amortizes fully. With negative amortization, the payment is smaller than the interest due, so the unpaid interest is added to the balance and you owe more after paying than before. The CFPB warns that this can leave you owing more than the home is worth. An interest-only loan pays just the interest for a set period, so the balance doesn’t fall at all until principal payments begin, and then the payment jumps. A balloon loan is paid on a long schedule but comes due early, leaving a large final payment that many borrowers can meet only by selling or refinancing.

Federal rules keep these features out of the general Qualified Mortgage category: payments must be substantially equal and must not increase the principal, defer principal or, apart from limited exceptions, end in a balloon payment. They still appear in some other home loans, business loans and personal debts. MoneyWhatIf’s debt and repayment guide shows the effect with a $10,000 balance at 12% and an $80 payment, which leaves $10,020 owed after the first month.

The word also describes spreading a cost over time. In business taxes, section 197 of the Internal Revenue Code lets a buyer deduct the cost of goodwill and many other acquired intangibles evenly over 15 years, starting in the month of acquisition. For homeowners, mortgage points that can’t be deducted in the year paid, including most points on a refinance, are deducted evenly over the life of the loan.

Retirement savers meet the idea in the fixed amortization method for 72(t) substantially equal periodic payments. The IRS lets you set a level annual withdrawal from an IRA as if the balance were a loan being paid off over your life expectancy, at an interest rate up to the greater of 5% or 120% of the federal mid-term rate. The formula that sets a mortgage payment sets that withdrawal. The same logic appears in Decumulation planning: spending a portfolio down to zero over a chosen number of years at an assumed return is an amortization problem.