Two ways to pay back the same loan
When you borrow a fixed sum and repay it in monthly installments, the lender needs to know how each payment is split between interest (the price of borrowing) and principal (the money you actually owe back). Two schedules cover most consumer installment loans, such as auto loans, personal loans and fixed-rate mortgages. With equal payment, also called an amortizing or level-payment loan, you pay the same total every month. With equal principal, sometimes called constant-amortization, you pay back the same slice of principal every month, plus interest on whatever is still outstanding. This calculator runs both on identical inputs so you can see the monthly cash-flow difference and the total interest difference at the same time.
A third structure, interest-only (or bullet) repayment, keeps the principal untouched until the end. Monthly cost is the lowest, but the balance never shrinks, so total interest is the highest. That structure is not modeled here; for a rough monthly figure, multiply the balance by the annual rate and divide by 12.
- Equal payment: the payment is flat, so it is easy to budget. In the early months most of each payment is interest, and the share of principal grows later. The balance falls slowly at first.
- Equal principal: the payment starts high and drops every month by a fixed amount. You build equity faster and pay less total interest, but the first payments are the heaviest.
How the numbers are calculated
Let r be the monthly rate (annual rate Γ· 12 Γ· 100) and n the number of monthly payments. This calculator uses simple monthly compounding, which is the standard textbook model. Real lenders may calculate interest by day or use a slightly different convention, so their figures can differ by small amounts.
Equal-payment monthly payment = P Γ r Γ (1 + r)n Γ· ((1 + r)n β 1)
This is the single amount A that makes the present value of n equal payments, discounted at the monthly rate, add up exactly to the loan P. Each month, interest is the previous balance times r. Whatever is left of the payment reduces principal, and the new balance is the old balance minus that principal portion. After n payments the balance reaches zero.
Equal principal: principal portion = P Γ· n every month; interest in month k = remaining balance Γ r. The first payment is P Γ· n + P Γ r, and each later payment is smaller by (P Γ· n) Γ r. Total interest has a closed form: P Γ r Γ (n + 1) Γ· 2.
At a 0% rate both methods collapse to P Γ· n per month with no interest, and the calculator handles that case directly.
Worked examples (checked by hand and with code)
Example 1: $200,000 at 6% for 30 years (360 months). The monthly rate is 0.5%. The equal-payment amount is about $1,199.10, so the total repaid is about $431,676 and the total interest is about $231,676, which is 115.8% of the amount borrowed. In month 1 the interest is $1,000.00 and only $199.10 goes to principal, leaving a balance of about $199,800.90. In month 2 the interest is $999.00. Under equal principal the first payment is about $1,555.56 and the last about $558.33, with total interest of $180,500. The difference is about $51,176 in interest, paid for by a first payment that is roughly $356 higher.
Example 2: $20,000 at 7.5% for 60 months. The monthly rate is 0.625%. The equal-payment amount is about $400.76 and the total interest about $4,045.54. Month 1 interest is $125.00 and principal $275.76. The equal-principal route starts at about $458.33, ends near $335.42, and costs about $3,812.50 in interest, so the gap is only around $233. On a short, small loan the choice of method matters far less than the rate or the term.
Both examples can be reproduced with the formulas above. The equal-principal interest total was also confirmed by summing month-by-month interest, which matches the closed form.
Monthly payment reference table ($100,000, equal payment)
The table below is computed with the formula when the page is built. Scale it linearly: a $250,000 loan costs 2.5 times as much per month as the $100,000 row. Compare columns to see how stretching the term lowers the monthly payment, and compare rows to see what one percentage point of rate does.
| Annual rate | 1 yr | 3 yr | 5 yr | 10 yr | 15 yr | 20 yr | 30 yr |
|---|---|---|---|---|---|---|---|
| 3% | $8,469 | $2,908 | $1,797 | $966 | $691 | $555 | $422 |
| 4% | $8,515 | $2,952 | $1,842 | $1,012 | $740 | $606 | $477 |
| 5% | $8,561 | $2,997 | $1,887 | $1,061 | $791 | $660 | $537 |
| 6% | $8,607 | $3,042 | $1,933 | $1,110 | $844 | $716 | $600 |
| 7% | $8,653 | $3,088 | $1,980 | $1,161 | $899 | $775 | $665 |
How the term changes total interest ($100,000 at 6%)
| Term | Monthly payment | Total interest | Interest as % of loan |
|---|---|---|---|
| 5 yr | $1,933 | $15,997 | 16.0% |
| 10 yr | $1,110 | $33,225 | 33.2% |
| 15 yr | $844 | $51,894 | 51.9% |
| 20 yr | $716 | $71,943 | 71.9% |
| 30 yr | $600 | $115,838 | 115.8% |
Moving from 30 years to 15 years raises the monthly payment but cuts total interest by more than half in this example. A lower monthly payment is not the same as a cheaper loan, because you are paying interest on the balance for a longer time.
Common mistakes
- Entering years instead of months. The term field takes months. Multiply years by 12: 5 years is 60, 15 years is 180, 30 years is 360.
- Comparing the APR with the note rate. Many lenders advertise an annual percentage rate that bundles in some fees. This tool takes a plain interest rate, so enter the note rate for the payment and treat fees separately.
- Judging by the monthly payment alone. Two loans with similar payments can have very different total interest and payoff speeds.
- Expecting fast principal reduction in an equal-payment loan. In Example 1 only about 17% of the first payment reduces the balance. Extra payments in the early years have an outsized effect.
- Assuming the rate never changes. With an adjustable rate, recompute using the remaining balance and remaining months after each reset.
When this calculator is not enough
- Adjustable-rate or variable-rate loans where the total cost depends on future rate changes.
- Loans with an interest-only period, balloon payment, or negative amortization.
- Costs outside principal and interest: origination or closing fees, insurance, taxes, prepayment penalties and late fees.
- Revolving credit such as credit cards or lines of credit, where the balance and the payment change month by month.
Using the results
- Start from what you can afford. Look at the monthly figure first. If it strains your budget, adjust the amount, the term or the rate you are shopping for rather than hoping the numbers work out.
- Test extra payments. Because early payments are mostly interest, shortening the term even a little changes total cost noticeably. Re-run the calculation with a shorter term to see the saving.
- Compare offers on the same inputs. Enter each lender's rate and term, then add that lender's fees on top to get a fair comparison.
- Check savings alternatives. If you are weighing paying down debt against saving, see the compound interest calculator, the deposit interest calculator or the savings installment calculator.
Important notes
This calculator produces a reference estimate from the principal, rate and term you enter. It is not financial, legal or tax advice, and it is not an offer of credit. Rates in the examples are assumptions chosen for illustration and do not describe any real product. Actual payments depend on the lender's day-count convention, rounding, fees, insurance, promotional rates and your credit profile. Confirm important decisions with the lender and the official loan disclosure. Everything you type is computed in your browser and is not sent to a server.
Frequently Asked Questions
Which repayment method is better?
On total interest alone, equal principal always costs less for the same rate and term. But its early payments are larger, which can strain a budget or reduce how much a lender will approve. Equal payment gives a predictable monthly figure, which is why it is the more common choice.
Does this include fees, insurance or prepayment penalties?
No. Only principal and interest are calculated. Closing costs, origination fees, insurance and any prepayment penalty are separate and should be added to the lender's quoted figures when you compare offers.
Can I use it for a variable-rate loan?
The tool assumes one fixed rate for the whole term. For an adjustable loan, run it again at each reset using the remaining balance, the new rate and the months left, and you get an estimate of the payment from that point forward.
How much does a one-point rate increase add to the payment?
The reference table shows it. On $100,000 over 30 years, 5% gives about $536.82 per month and 6% about $599.55, an increase of roughly $63 per month for every $100,000 borrowed.
Why does my lender's figure differ by a few dollars?
Lenders may accrue interest daily, handle a short first period differently, or round each payment. These conventions create small differences, usually a few dollars a month, from the textbook monthly-compounding result used here.
How do I enter a term given in years?
Multiply by 12. Three years is 36 months, ten years is 120, and thirty years is 360.