About

Amortization distributes a fixed loan payment between interest cost and principal reduction over n periods. The split is non-linear: early payments allocate over 70% to interest on a typical 30-year mortgage. Misunderstanding this front-loading effect leads borrowers to overestimate equity growth and underestimate total interest exposure. This calculator generates a complete month-by-month schedule using the standard annuity formula, accepting optional extra principal payments that compress the effective term and reduce lifetime interest. Results assume a fixed rate with no refinancing or rate adjustment.

Precision matters. A 0.25% rate error on a $300,000 loan compounds to roughly $15,000 in miscalculated interest over 30 years. The schedule produced here rounds to the cent at each iteration rather than applying a single end-of-term rounding, matching the method used by most US lending institutions under TILA (Truth in Lending Act) disclosure requirements. Note: this tool assumes monthly compounding and does not model daily interest accrual, adjustable rates, or escrow.

Formulas

The fixed monthly payment M for a fully amortizing loan is derived from the present value of an ordinary annuity:

M = P ⋅ r⋅(1 + r)ⁿ(1 + r)ⁿ − 1

Where P is the loan principal (initial balance), r is the periodic (monthly) interest rate equal to the annual rate divided by 12, and n is the total number of monthly payments (term in years × 12).

For each payment period k, the interest portion and principal portion are computed iteratively:

I_k = B_k−1 ⋅ r

P_k = M − I_k + E

B_k = B_k−1 − P_k

Where I_k is interest for month k, B_k is the remaining balance after month k, P_k is the principal paid in month k, and E is the optional extra monthly payment applied directly to principal. When E > 0, the loan terminates early at the month where B_k ≤ 0.

Reference Data

Loan Type	Typical Term	Typical Rate Range (US 2024)	Common Loan Amount	Total Interest (est.)	Monthly Payment (est.)
30-Year Fixed Mortgage	360 mo	6.5 - 7.5%	$300,000	$383,139	$1,896
15-Year Fixed Mortgage	180 mo	5.8 - 6.8%	$300,000	$162,240	$2,568
5/1 ARM (initial period)	60 mo fixed	5.5 - 6.5%	$300,000	Variable after yr 5	$1,703
Auto Loan (New)	60 - 72 mo	5.0 - 7.5%	$35,000	$5,600	$676
Auto Loan (Used)	48 - 60 mo	6.5 - 10.0%	$22,000	$4,800	$447
Personal Loan	36 - 60 mo	8.0 - 15.0%	$15,000	$4,000	$528
Student Loan (Federal)	120 mo	5.5 - 7.0%	$37,000	$11,400	$403
Student Loan (Private)	120 - 180 mo	4.0 - 14.0%	$50,000	$18,000	$567
Small Business Loan (SBA 7a)	120 - 300 mo	10.0 - 13.0%	$250,000	$200,000+	$3,587
Home Equity Loan	60 - 180 mo	7.5 - 10.0%	$50,000	$22,000	$600
Boat / RV Loan	120 - 240 mo	6.0 - 9.0%	$80,000	$38,000	$983
Medical / Dental Loan	24 - 60 mo	5.0 - 25.0%	$10,000	$2,700	$265
Construction Loan	12 - 18 mo	8.0 - 12.0%	$400,000	Interest-only phase	Varies (draw schedule)

Frequently Asked Questions

Extra payments reduce the outstanding balance B_k immediately. Since interest each month is calculated as B_k−1 ⋅ r, a lower balance produces less interest in every subsequent period. On a $300,000 loan at 7% over 30 years, adding just $200/month extra saves approximately $115,000 in interest and shortens the loan by roughly 8 years.

The annuity formula produces a fixed payment M, but the interest component I_k shrinks as B_k decreases. In month 1 of a 30-year $300,000 mortgage at 7%, approximately $1,750 goes to interest and only $146 to principal. By month 300, this reverses. The crossover point (where principal exceeds interest) typically occurs around 60% - 70% through the loan term.

No. This tool models fixed-rate amortization only. An ARM requires re-computation of M at each rate adjustment interval using the remaining balance and remaining term as new inputs. For the fixed initial period of a 5/1 ARM, you can use this calculator with the introductory rate and a term equal to the full loan length, but results beyond year 5 will diverge from actual ARM behavior.

Each monthly payment is rounded to the nearest cent. This cumulative rounding means the final payment rarely equals M exactly. The calculator adjusts the last payment to zero out the balance precisely, which may result in a final payment slightly higher or lower than the standard amount. This matches TILA disclosure methodology used by US lenders.

If you are past the crossover point where more than 50% of each payment goes to principal, refinancing to a new loan resets the amortization curve, front-loading interest again. The break-even depends on closing costs divided by monthly savings. For example, $4,000 in closing costs with $150/month savings gives a break-even of approximately 27 months. Use the schedule to check how much interest remains versus principal before refinancing.

Not directly. Biweekly payments effectively make 13 full monthly payments per year instead of 12. To approximate this effect, set the extra monthly payment to M12 (one-twelfth of the monthly payment). This closely replicates the biweekly acceleration without changing the compounding model.