Amortization is how most real-world loans are paid off. Instead of paying interest forever or paying everything at once, you make a series of regular payments (usually monthly). Each payment covers two things:
- Interest on the outstanding loan balance
- Principal reduction (the part that actually pays the loan down)
Over time, the balance gets smaller, so the interest portion of your payment usually shrinks. That means more of each payment goes toward principal as the loan progresses.
This article explains amortization in plain language, shows how an amortization schedule is built, and includes step-by-step examples you can verify.
What Is Amortization?
Amortization is the process of paying off a loan through regular payments over a set term. The word is used in two common ways:
- Amortized loan: A loan designed to be fully paid off by the end of the term using fixed payments.
- Amortization schedule: A table showing every payment, how much goes to interest, how much goes to principal, and what balance remains after each payment.
Most mortgages, many auto loans, personal loans, and business term loans are amortized.
Why Amortization Matters
Understanding amortization helps you:
- estimate your monthly payment
- see how much interest you’ll pay over time
- understand why early payments feel “mostly interest”
- compare loan offers beyond the interest rate
- measure the impact of extra payments
- plan refinancing decisions
A loan with a lower payment can still cost more overall if the term is longer or the rate is higher.
Core Inputs for Amortization Calculations
You’ll typically need:
- P = loan principal (amount borrowed)
- APR_percent = annual interest rate in percent (example: 6 for 6%)
- APR = annual interest rate in decimal
- payments_per_year = 12 for monthly (common), 26 for biweekly, 52 for weekly
- i = periodic interest rate (APR / payments_per_year)
- years = loan term in years
- n = total number of payments (years * payments_per_year)
- PMT = payment amount per period
- balance = remaining loan balance before/after each payment
Step 1: Convert APR to Periodic Interest Rate
APR = APR_percent / 100
i = APR / payments_per_year
n = years * payments_per_year
Example: 6% APR with monthly payments
APR_percent = 6
APR = 6/100 = 0.06
payments_per_year = 12
i = 0.06/12 = 0.005
That periodic rate i is what you apply each period to the balance.
Step 2: Calculate the Fixed Payment (PMT)
For a fully amortizing loan with fixed payments:
PMT = P * (i * (1 + i)^n) / ((1 + i)^n - 1)
Edge case if interest rate is 0:
if i == 0:
PMT = P / n
This PMT is designed so the loan ends at (or extremely close to) zero after n payments (rounding can cause tiny differences).
What Happens Inside Each Payment?
Each payment is split into:
interest_payment = balance * i
principal_payment = PMT - interest_payment
new_balance = balance - principal_payment
That’s the entire engine of an amortization schedule.
At the beginning of the loan:
- balance is high
- interest_payment is high
- principal_payment is smaller
Later in the loan:
- balance is lower
- interest_payment decreases
- principal_payment increases
Example 1: Full Amortization Schedule (12-Month Mini Loan)
Let’s use a small example so the schedule is easy to follow.
Loan:
- P = 12,000
- APR_percent = 12
- payments_per_year = 12 (monthly)
- years = 1
- n = 12 payments
1) Compute i and PMT
P = 12000
APR_percent = 12
payments_per_year = 12
years = 1
APR = 12/100 = 0.12
i = APR / 12 = 0.12/12 = 0.01
n = years * 12 = 12
PMT = P * (i * (1 + i)^n) / ((1 + i)^n - 1)
PMT = 12000 * (0.01 * (1.01)^12) / ((1.01)^12 - 1)
PMT works out to about 1,066.19 (rounded to cents).
We’ll build the schedule using:
interest_payment = balance * i
principal_payment = PMT - interest_payment
new_balance = balance - principal_payment
2) Start schedule (first few payments)
1st Payment:
balance = 12000.00
interest_payment = 12000.00 * 0.01 = 120.00
principal_payment = 1066.19 - 120.00 = 946.19
new_balance = 12000.00 - 946.19 = 11053.81
2nd Payment:
balance = 11053.81
interest_payment = 11053.81 * 0.01 = 110.54
principal_payment = 1066.19 - 110.54 = 955.65
new_balance = 11053.81 - 955.65 = 10098.16
3rd Payment:
balance = 10098.16
interest_payment = 10098.16 * 0.01 = 100.98
principal_payment = 1066.19 - 100.98 = 965.21
new_balance = 10098.16 - 965.21 = 9132.95
Notice what’s happening:
- interest goes down each month
- principal goes up each month
- balance falls faster as time goes on
That’s amortization.
3) General schedule loop (calculator logic)
balance = P
for payment_number from 1 to n:
interest_payment = balance * i
principal_payment = PMT - interest_payment
balance = balance - principal_payment
In real calculators, you also round currency values each period.
Example 2: Mortgage-Style Amortization (Realistic)
Now let’s use a more common scenario.
Loan:
- P = 300,000
- APR_percent = 6
- monthly payments
- term = 30 years
1) Compute i, n, PMT
P = 300000
APR_percent = 6
payments_per_year = 12
years = 30
APR = 0.06
i = 0.06/12 = 0.005
n = 30*12 = 360
PMT = 300000 * (0.005 * (1.005)^360) / ((1.005)^360 - 1)
This gives a monthly payment around 1,798.65 (principal + interest only).
2) First payment breakdown (approx)
balance = 300000.00
interest_payment = 300000.00 * 0.005 = 1500.00
principal_payment = 1798.65 - 1500.00 = 298.65
new_balance = 300000.00 - 298.65 = 299701.35
That’s why early mortgage payments feel “mostly interest.” The balance is large, and even a moderate rate creates a big interest charge each month.
3) Later payment behavior (what changes)
As the balance falls, interest becomes smaller:
interest_payment = balance * i
So the same PMT leaves more room for principal.
This shift is the “amortization curve.”
What Is an Amortization Schedule?
An amortization schedule is typically a table with these columns:
- Payment number
- Payment amount (PMT)
- Interest portion
- Principal portion
- Remaining balance
In short form:
payment_no | PMT | interest | principal | balance
A full schedule shows every payment from 1 to n.
How to Calculate Remaining Balance After k Payments
Instead of generating the full schedule, you can compute the balance after k payments directly.
balance_k = P * (1 + i)^k - PMT * (((1 + i)^k - 1) / i)
Where:
- k = number of payments already made
- i = periodic rate
- PMT = periodic payment amount
This is useful for payoff quotes, refinance comparisons, and building summary views.
Total Interest Paid Over the Loan
Once you know PMT:
total_paid = PMT * n
total_interest = total_paid - P
This is the simplest way to understand the full cost of a loan.
Example concept:
- if PMT is lower because term is longer, total_paid can become much higher.
Amortization vs Simple Interest (Important Distinction)
Simple interest (basic form) is:
I = P * r * t
A = P + I
Amortization is different because:
- interest is computed repeatedly each period
- the principal decreases each payment
- the interest portion changes over time
Amortized loans can still be described as “simple interest loans” in some lending contexts (interest accrues on the outstanding balance without compounding interest-on-interest), but the payment structure is amortized. The schedule is still built using periodic interest on remaining balance.
Extra Payments and Amortization (How They Change the Schedule)
Extra payments usually go directly toward principal. That reduces the balance sooner, which reduces future interest.
If you add extra each period:
PMT_effective = PMT + extra
principal_payment = PMT_effective - interest_payment
This can shorten the loan term and reduce total interest dramatically.
Simple way to estimate savings
- Extra principal reduces balance sooner
- Lower balance means lower interest every following period
For accurate results, you rebuild the schedule with the extra payment.
Common Amortization Mistakes
1) Mixing APR with periodic rate
APR is annual. For monthly payments you must divide by 12.
i = APR / 12
2) Incorrect payment count
30-year monthly loan has:
n = 30 * 12 = 360
3) Not rounding currency consistently
Many lenders round interest and principal to cents each period. If you don’t, your end balance may not be exactly zero.
4) Forgetting that taxes/insurance are not part of amortization
Mortgage escrow (taxes/insurance) may be added to your monthly bill, but it’s not part of the loan amortization math.
Frequently Asked Questions (Amortization)
What does amortization mean in simple terms?
It means paying off a loan over time with regular payments that include interest and principal.
Why do early payments go mostly to interest?
Because interest is calculated on the current balance, and the balance is highest at the beginning.
Does the payment amount change every month?
For a fixed-rate amortized loan, the payment (PMT) is usually constant. The interest and principal portions change, but the total payment stays the same.
How do I make an amortization schedule?
You calculate PMT, then for each period compute interest = balance * i, principal = PMT – interest, and update balance.
Do extra payments reduce interest?
Yes. Extra payments reduce principal earlier, which reduces the balance and the future interest portion.
Summary
Amortization is the standard method used to pay off loans through regular payments that gradually reduce the balance. The key formulas are:
APR = APR_percent / 100
i = APR / payments_per_year
n = years * payments_per_year
PMT = P * (i * (1 + i)^n) / ((1 + i)^n - 1)
interest_payment = balance * i
principal_payment = PMT - interest_payment
new_balance = balance - principal_payment
Once you understand those, you can build an amortization schedule, compute remaining balances, estimate total interest, and model extra payments with confidence.
