How to calculate amortization, step by step
Amortization is one number that answers one question: what is the equal monthly payment that pays off a loan, interest and all, over its term? The calculation needs three numbers: your loan amount, your annual rate and your term in years. On a $300,000 loan at 6.5% over 30 years, the monthly payment is $1,896.20, the total interest is $382,633.47 and the total paid is $682,633.47. So the monthly payment is the loan amount times the monthly rate times one plus the monthly rate to the power of the number of payments, divided by one plus the monthly rate to the power of the number of payments minus one.
The definition is the equal payment that clears the loan: each month the lender charges interest on the balance still owed, and the rest of the payment chips away at the balance. The monthly rate is the annual rate divided by 12 — 6.5% a year is 0.541667% a month — and the number of payments is the term in years times 12 — 30 years is 360 payments. If you divide the annual rate by 12 and forget the power, the payment comes out wrong, and the schedule that follows is built on a number that is not honest.
The worked example, line by line. Step 1 — the monthly rate: 6.5% ÷ 12 = 0.541667% a month. Step 2 — the number of payments: 30 × 12 = 360 payments. Step 3 — the monthly payment: $300,000 × 0.00541667 × (1.00541667)360 ÷ ((1.00541667)360 − 1) = $1,896.20. Step 4 — the first month: interest $300,000 × 0.00541667 = $1,625.00, principal $1,896.20 − $1,625.00 = $271.20, balance $300,000 − $271.20 = $299,728.80. Step 5 — the first year: interest $19,401.27, principal $3,353.18, balance $296,646.82. Step 6 — the totals: $1,896.20 × 360 = $682,633.47 paid, of which $382,633.47 is interest. Work it yourself in the amortization calculator.
A note on the rounding: the figures are displayed to two decimals, half-up. The payment is $1,896.20 displayed and $1,896.204070 unrounded, and the total interest is $382,633.47 displayed and $382,633.465372 unrounded — with fractional inputs it can land a hair either side of a round number, and the calculator prints the unrounded figure so the rounding does not mislead you.
What the answer means
A monthly payment of $1,896.20 means you pay $1,896.20 every month for 30 years — 360 payments, $682,633.47 in total — and the loan is gone at the end. That $682,633.47 has to cover everything the loan costs: the $300,000 you borrowed and the $382,633.47 of interest on top, which is more than the loan itself. The first year is almost all interest — $19,401.27 of interest against $3,353.18 of principal — so after a year of payments you still owe $296,646.82 of the $300,000. A $1,896.20 payment that is mostly interest in the first year is normal, not a mistake, and the balance falls faster as the years pass. Work it out in the amortization calculator.
Why the interest is front-loaded
The interest is front-loaded because the lender charges interest on the balance still owed, and the balance is biggest at the start. In month 1 the balance is $300,000, so the interest is $1,625.00 and the principal is only $271.20. By month 12 the balance is $297,220.89, so the interest is $1,611.49 and the principal is $284.72 — and by the last month the interest is a few dollars and almost the whole payment is principal. The payment never changes, but the split inside it does: the interest shrinks as the balance shrinks, and the principal grows to fill the gap. That is why an extra payment early saves so much interest — it cuts the balance that every later month’s interest is charged on.
Amortization vs interest-only
Amortization and interest-only answer different questions, and mixing them up is the most common mistake. Amortization pays the loan off — $1,896.20 a month here, and the balance is $0 after 30 years. Interest-only pays just the interest — $1,625.00 a month here, and the balance is still $300,000 after 30 years. One ends the loan, the other never does. The same $300,000 at 6.5% costs $1,625.00 a month interest-only and $1,896.20 a month amortized — the $271.20 difference is the principal, and it is what actually pays the loan down. Use amortization when you want the loan gone, and use interest-only only when you understand that the balance never moves. Work it out in the amortization calculator.
Amortization vs the payoff schedule
The amortization formula and the payoff schedule answer different questions too. The formula gives the payment — $1,896.20 a month here. The schedule gives the month-by-month split — month 1: $1,625.00 interest, $271.20 principal, $299,728.80 balance; month 12: $1,608.40 interest, $287.81 principal, $296,646.82 balance. One is a number, the other is a table. A $1,896.20 payment with a $1,625.00 first month of interest is the same loan seen two ways — the formula tells you what to pay, and the schedule tells you where it goes. Use the formula when you want the payment, and use the schedule when you want to see the balance fall. Work it out in the amortization calculator, and check the loan payoff calculator and the mortgage calculator before you decide what the answer means.
Common mistakes
The first mistake is dividing the annual rate by 12 and forgetting the power — only the full formula counts toward the payment, so use the monthly rate and the number of payments together, not the rate alone. The second is confusing the payment with the principal — a $1,896.20 payment is not $1,896.20 of principal, and in month 1 only $271.20 of it is principal. The third is forgetting that the term is in months — a 30-year loan is 360 payments, not 30, and the formula needs the months. The fourth is assuming the interest stays the same — it falls every month as the balance falls, and a payment that is mostly interest in year 1 is mostly principal by year 25. Work it out in the amortization calculator, and check the loan payoff calculator and the compound interest calculator before you decide what the answer means.