Loans
How To Calculate An Amortization Schedule
An amortization schedule is the month-by-month ledger of a fixed-rate loan: every payment is the same size, but the split between interest and principal shifts a little each month. Early on almost everything goes to interest; near the end almost everything goes to principal. The monthly payment comes from one formula, and from it you can read off the first month's interest, the principal that payment retires, and the balance left afterwards.
Quick Answer
M = P x r / (1 - (1 + r)^-n)
- P
- Amount borrowed after any down payment
- r
- Monthly interest rate, the annual nominal rate divided by 12
- n
- Total number of monthly payments, years times 12
- M
- Fixed monthly payment of principal and interest
Divide the annual rate by 12 to get the monthly rate r, multiply the term in years by 12 to get the number of payments n, then apply M = P x r / (1 - (1+r)^-n). For a $20,000 loan at 6% over 5 years: r = 0.005, n = 60, and M = 20000 x 0.005 / (1 - 1.005^-60) = 386.66. The first payment's interest is 0.005 x 20000 = 100.00, so 286.66 goes to principal and the balance falls to 19,713.34.
What Is An Amortization Schedule?
A fixed-rate amortization schedule tables every payment of a loan and the interest and principal inside it. The loan is a reducing-balance instrument: interest is charged on whatever you still owe, so as the balance falls the interest portion falls with it, and the fixed payment therefore retires more principal each month.
The schedule is not a projection of extra payments or variable rates; it describes the contract as written. Lenders publish one with every mortgage, car loan and personal loan, and the total interest line at the bottom is the number that tells you what borrowing really cost.
The single most important idea is that the payment is calculated so that the present value of all the payments equals the amount borrowed. Discount each future payment back at the monthly rate, add them up, and the total is exactly the principal. That is the definition the formula encodes, and it is why the payment depends on all three of principal, rate and term at once.
Consider a 20,000 loan at 6% over five years. The monthly rate is 0.005 and there are 60 payments. The payment works out to 386.66. The first month the lender charges 0.005 times 20,000, which is 100.00 of interest, so only 286.66 of your 386.66 actually reduces the debt and the balance becomes 19,713.34. In month two the interest is charged on 19,713.34 instead of 20,000, so it drops a fraction, and the principal portion rises by the same fraction. That tiny shift repeats sixty times and is the entire mechanism.
The early skew surprises everyone. On a thirty-year mortgage at a typical rate the first payment can be eighty per cent interest. The reason is not a trick; it is arithmetic. When the balance is large, the interest on it is large, and the leftover for principal is small. As the balance shrinks the interest shrinks and the leftover grows. By the final year the split has reversed and almost the whole payment is principal.
Total interest is the price of that skew. Multiply the payment by the number of payments and subtract the principal. For the 20,000 loan above the total paid is 60 times 386.66, which is 23,199.60, so the interest is 3,199.60. Stretch the same loan to ten years at the same rate and the payment falls but the total interest roughly doubles, because you are renting the lender's money for twice as long.
An amortization schedule is also the natural home for extra payments. Any amount above the scheduled payment goes straight to principal, which lowers every future interest charge. One extra full payment a year on a thirty-year mortgage can cut the term by four or five years and save tens of thousands in interest, and the schedule shows precisely where those savings land.
The formula assumes the rate never changes, the payment is never missed and interest is charged monthly on the reducing balance. Real statements round every month, so a hand calculation and a lender's total differ by a few cents. Those cents are rounding, not an error in the method.
Formula
M = P x r / (1 - (1 + r)^-n)
P is the amount borrowed, r the monthly rate and n the number of monthly payments. The denominator is the present-value factor of an annuity, which is why the same formula covers every fixed-rate loan.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal borrowed | currency | Amount borrowed after any down payment. |
| r | Monthly rate | rate | Annual nominal rate divided by 12. |
| n | Number of payments | count | Term in years multiplied by 12. |
| M | Monthly payment | currency | The fixed payment covering interest and principal. |
I1 = P x r ; Pr1 = M - I1
Interest for a month is the opening balance times the monthly rate; whatever is left of the payment reduces the balance.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| I1 | First-month interest | currency | Charged on the full opening balance. |
| Pr1 | First-month principal | currency | Payment minus interest. |
B1 = P - Pr1
The balance falls by exactly the principal portion of the payment.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B1 | Balance after first payment | currency | Opening principal less first-month principal. |
How To Calculate An Amortization Schedule
- 1
Convert the rate to monthly
A 6% annual nominal rate is 0.06 / 12 = 0.005 a month. Using 6% directly charges six percent every month and makes the payment look about twelve times too large.
- 2
Count the payments
Five years is 5 x 12 = 60 monthly payments. A 30-year mortgage is 360; the count, not the years, is what the formula wants.
- 3
Apply the payment formula
Compute (1+r)^-n first, subtract it from 1, then divide. For 20,000 at 0.005 over 60 months the payment is 386.66.
- 4
Split the first payment
Interest is 0.005 x 20000 = 100.00. Subtract it from the payment to get the principal portion, 286.66.
- 5
Roll the balance forward
Reduce the balance by the principal portion to get 19,713.34. Repeat for month two on the new balance; the interest shaves down every month.
Examples
Example 1: The default case: 20,000 at 6% over 5 years
- Loan amount
- 20,000
- Annual rate
- 6%
- Term
- 5 years
| Step | Calculation | Result |
|---|---|---|
| Number of payments | 5 x 12 | 60 |
| Monthly rate | 0.06 / 12 | 0.005 |
| Monthly payment | M = 20000 x 0.005 / (1 - 1.005^-60) | 386.66 |
| First-month interest | 20000 x 0.005 | 100.00 |
| Principal in payment one | 386.66 - 100.00 | 286.66 |
| Balance after payment one | 20000 - 286.66 | 19713.34 |
Result: The monthly payment is 386.66; month one sends 100.00 to interest and 286.66 to principal, leaving 19,713.34.
Example 2: A 35,000 car loan at 7.5% over 6 years
- Loan amount
- 35,000
- Annual rate
- 7.5%
- Term
- 6 years
| Step | Calculation | Result |
|---|---|---|
| Number of payments | 6 x 12 | 72 |
| Monthly rate | 0.075 / 12 | 0.00625 |
| Monthly payment | M = 35000 x 0.00625 / (1 - 1.00625^-72) | 605.11 |
| First-month interest | 35000 x 0.00625 | 218.75 |
| Principal in payment one | 605.11 - 218.75 | 386.36 |
| Balance after payment one | 35000 - 386.36 | 34613.64 |
Result: The payment is 605.11; interest takes 218.75 of the first one, so the balance only drops to 34,613.64.
Calculator
Monthly payment
$386.66
- Number of payments
- 60
- First-month interest
- $100.00
- Principal in payment one
- $286.66
- Balance after payment one
- $19,713.34
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the An Amortization Schedule calculator page.
Common Mistakes
Using the annual rate as the monthly rate
Forgetting to divide 6% by 12 turns a 386.66 payment into a nonsense figure near 60,000. Always divide the nominal annual rate by 12 before it enters the formula.
Counting years instead of payments
The exponent n is the number of monthly payments, 60 for five years, not the number of years. Substituting 5 gives a payment far too low.
Assuming the first payment is mostly principal
On a long loan the first payment is mostly interest. On 20,000 at 6% it is 100 interest against 286.66 principal; on a 30-year mortgage the interest share is even more lopsided.
Adding the interest rate to the principal
Simple interest adds P x r per year; amortized loans charge r on the declining balance, so the total interest is much less than P x rate x years.
Ignoring fees and insurance
The schedule covers principal and interest only. Origination fees, mortgage insurance and taxes sit outside it and change your real cash outflow.
Treating extra payments as automatic
A schedule built from the contract assumes no extra payments. Paying more shortens the term and cuts total interest, but you have to model that separately.
FAQ
What is an amortization schedule?
A table of every payment on a fixed-rate loan showing how much of each goes to interest and how much to principal, with the running balance. The payment stays constant; the split shifts toward principal over time.
Why is so much of my early payment interest?
Interest is charged on the outstanding balance. At the start the balance is at its largest, so the interest slice is at its largest too. On 20,000 at 6%, month one is 100 interest and only 286.66 principal.
Does the monthly payment change over the term?
Not on a fixed-rate loan. The payment is constant; only the interest and principal split moves. Adjustable-rate loans reset the rate, which does change the payment.
How much total interest will I pay?
Multiply the payment by the number of payments and subtract the principal. For 20,000 at 6% over 60 months that is 60 x 386.66 - 20,000 = 3,199.60 in interest.
Do extra payments help?
A lot. An extra payment goes straight to principal, which cuts the balance future interest is charged on. Even one extra payment a year can shave years off a mortgage.
What does the formula assume?
A fixed rate, a fixed payment, no fees, no extra payments and interest charged monthly on the reducing balance. Real statements round each month, so totals differ by a few cents.
References
- [1]Consumer Financial Protection Bureau, What is amortization? — https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-en-1949/
- [2]Investopedia, Amortization Schedule — https://www.investopedia.com/terms/a/amortization.asp
- [3]Federal Reserve, Consumer Credit release — https://www.federalreserve.gov/releases/g19/current/