How this amortization calculator works
Mortgages, auto loans and most personal loans are installment loans: you borrow a fixed amount and repay it with equal monthly payments over a set term. The payment never changes, but what it pays for does. Each month the lender first takes the interest owed on the remaining balance, and whatever is left of the payment reduces principal. This calculator builds that schedule payment by payment and shows the split for every row.
If you add extra principal, it is applied after the scheduled payment. The required payment stays the same, and the loan simply ends sooner. That is how most lenders treat prepayments, and it is why the chart shows two balance lines: the schedule you signed up for and the one your extra payment creates.
The amortization formula
The fixed monthly payment M that retires principal P in n payments at monthly rate r is:
r = annual rate ÷ 12, and n = years × 12. With a 0% rate, the payment is simply P ÷ n.
Each row of the schedule then follows three steps:
Principalt = M − Interestt
Bt = Bt−1 − Principalt
Every amount is rounded to the cent, and the final payment is adjusted so the balance lands on exactly $0.00. The step-by-step logic is explained further in how amortization schedules work.
Worked example: a $350,000, 30-year mortgage at 7.25%
The monthly rate is 0.0725 ÷ 12 = 0.0060417. Plugging that into the formula with n = 360 gives a principal-and-interest payment of $2,387.62.
- Payment 1: interest is $350,000.00 × 0.0060417 = $2,114.58, so only $273.04 reduces the balance.
- After 5 years: you have paid $143,257, but only $19,675 of it was principal. The balance is still $330,325.
- After 10 years: the balance is $302,086.
- Crossover: principal first exceeds interest at payment 246, about 20 years in.
- Lifetime interest: $509,539.14, on top of the $350,000 borrowed.
This front-loading is not a trick; it is what charging interest on a large balance looks like. It does mean that selling or refinancing in the first few years leaves you with most of the original balance still owed.
15-year vs. 30-year: the real trade-off
| $350,000 loan | Rate | Monthly P&I | Total interest |
|---|---|---|---|
| 30-year fixed | 7.25% | $2,387.62 | $509,539 |
| 15-year fixed | 6.5% | $3,048.88 | $198,797 |
The 15-year loan costs $661 more a month but saves $310,742 in interest, partly because shorter terms usually carry lower rates. The 30-year loan buys flexibility: you can still pay it like a shorter loan in good months and fall back to the lower required payment when money is tight. Rates in this example are illustrative; use the rate on your own Loan Estimate.
The same logic applies to smaller loans. A $15,000 personal loan at 12% costs $498.21 a month over 3 years with $2,936 of interest. Stretching it to 5 years lowers the payment to $333.67 but raises interest to $5,020.
Extra payments and bi-weekly schedules
A fixed monthly extra
Adding $200 a month to the example mortgage pays it off in 23 yr 7 mo and saves $129,530. Extra principal is most powerful early, because every dollar removed from the balance stops generating interest for the rest of the loan.
The “13th payment” effect of bi-weekly payments
Paying half the mortgage every two weeks produces 26 half-payments, or 13 full payments a year. You can get the same effect by adding one-twelfth of a payment, $198.97, to each monthly payment. On the example loan that cuts the term to 23 yr 7 mo and saves $129,055.
Recast or refinance?
A recast keeps your rate and term but recalculates the payment after a large lump-sum principal payment, usually for a small fee. A refinance replaces the loan with a new rate and term and comes with closing costs. Compare the closing costs with the monthly savings to find how many months it takes to break even, and remember that restarting a 30-year clock puts you back at the interest-heavy start of a new schedule.
What the monthly payment leaves out
For a mortgage, this calculator shows principal and interest only. Your actual monthly housing payment usually also includes property taxes and homeowners insurance held in escrow, and may include private mortgage insurance (PMI) if you put less than 20% down, plus HOA dues. Lenders often call the full amount PITI. For personal loans, an origination fee deducted from the loan proceeds raises the effective cost above the note rate; the APR on your disclosure includes it.
Assumptions and limits
- The interest rate is fixed for the life of the loan. Adjustable-rate mortgages will differ after the first reset.
- Interest accrues monthly at the annual rate ÷ 12, the convention for US mortgages and most installment loans.
- Extra principal is applied every month and does not change the required payment.
- Taxes, insurance, PMI, fees and late charges are not included.