Amortization is the way car loans, mortgages and most personal loans are repaid: a fixed payment every month for a set number of months. Each payment first covers the interest on the balance still owed; whatever is left reduces the principal. The CFPB notes that early in a loan more of each payment goes to interest, so the balance falls slowly at first and faster near the end. The table that lists the interest and principal in every payment is the amortization schedule.
Formula
M = P × r ÷ (1 − (1 + r)^−n)
Interest this month = balance × r
Principal this month = M − interest
- M is the monthly payment, P the amount borrowed, n the number of payments.
- r is the monthly rate: the APR as a decimal divided by 12.
Example
$30,000 borrowed at 7.54% for 60 months: r = 0.0754 ÷ 12 = 0.0062833, so M = $601.71. The first payment is $188.50 of interest (30,000 × 0.0062833) and $413.21 of principal. By the second month the balance is $29,586.79, interest drops to $185.90 and principal rises to $415.81. Over the full term, interest totals $6,102.53, of which $2,087.00 is paid in the first 12 months.
Common mistakes
- Assuming interest is spread evenly. In the example, the first year carries 34% of all interest and the last year 5%.
- Assuming extra payments always help. On a simple interest loan they cut the principal and future interest; on a precomputed interest loan, the CFPB warns, they do not reduce the interest owed.
See how to calculate interest on a car loan for the full year-by-year schedule, or use the TVM calculator to solve for the payment, term or rate.