Learning goals
- Identify interest, principal, and ending balance on a schedule row
- Explain why interest shrinks and principal grows across a fixed payment loan
- Estimate the effect of an extra principal payment on future interest
What the schedule is for
An amortization schedule is a table: one row per payment period. Typical columns are payment number, payment amount, interest portion, principal portion, and ending balance.
For a standard fixed installment loan, the payment amount stays the same (aside from a slightly adjusted final payment). Interest each period equals the starting balance times the periodic rate. Whatever remains of the payment after interest goes to principal.
Reading a few rows teaches more than staring at the payment formula. You can see how slowly principal falls at first on a long loan, and how extra principal payments shorten the table.
One period of amortization
interest = start balance × r; principal = payment − interest; end balance = start − principal
r is the rate per period (for monthly loans, annual rate ÷ 12). The next row’s starting balance is this row’s ending balance. Repeat until the balance reaches zero.
Example 1 — Build the first two rows
Given
Loan $5,000.00 12% APR, monthly payments, payment fixed at $444.24 for a short 12-month term. Show months 1–2.
Steps
- Monthly rate r = 0.12 / 12 = 0.01.
- Month 1 interest = 5,000 × 0.01 = $50.00; principal = 444.24 − 50 = $394.24; end balance = 5,000 − 394.24 = $4,605.76.
- Month 2 interest = 4,605.76 × 0.01 ≈ $46.06; principal ≈ 444.24 − 46.06 = $398.18; end balance ≈ $4,207.58.
Answer
Interest falls from $50.00 to about $46.00 while principal rises from $394.00 to $398.00.
Tip: Same payment, different split — that pattern continues for the whole schedule.
Example 2 — Find remaining balance after many payments
Given
You are comparing two quotes and only need the balance after 24 months — not every row by hand.
Steps
- Use an amortization calculator (or the closed-form remaining-balance formula) with principal, rate, term, and periods elapsed.
- Confirm the schedule’s month-24 ending balance matches the tool output.
- Total interest so far = sum of interest column for months 1–24 (or total paid − principal reduction).
Answer
Calculators generate the full table; spot-check early rows with interest = balance × r.
Tip: If a hand check of month 1 fails, the rate or payment input is wrong — fix inputs before trusting later rows.
Example 3 — Extra principal payment
Given
After the regular month-1 payment on the $5,000.00 loan, you pay an extra $500.00 toward principal.
Steps
- Regular month-1 ending balance was $4,605.76; subtract $500.00 → $4,105.76.
- Month 2 interest becomes 4,105.76 × 0.01 ≈ $41.06 instead of ~$46.06.
- Every later interest charge is computed on a lower balance, so the loan finishes earlier or with less total interest.
Answer
Extra principal cuts future interest immediately because interest is charged on what you still owe.
Tip: Confirm with the lender that extras apply to principal, not prepaid interest or fees.
Reading “payment” as all principal
Common mistake
Assume a $444.00 payment reduces the $5,000.00 balance by $444.00 in month 1.
Better approach
Only the principal column reduces the balance. Month 1 principal was $394.24; $50.00 was interest cost for using the money that month.
Comparing loans by first-month interest alone
Common mistake
Pick the loan with the lowest first-month interest without checking term, fees, or total interest.
Better approach
Use the full schedule (or totals): payment, term, APR, fees, and total interest paid over the life of the loan.
Check your understanding
1.Balance $10,000.00 monthly r = 0.005, payment $300.00. Month-1 interest and principal?
Answer: Interest $50.00; principal $250.00; end balance $9,750.00.
2.If interest this month is $40.00 and payment is $300.00 how much goes to principal?
Answer: $260.00.
3.Why does the interest column trend down on a fixed payment loan?
Answer: Balance falls, so balance × r shrinks each period.
4.What happens to next month’s interest if you pay extra principal today?
Answer: It decreases because the starting balance is lower.
Key takeaways
- Each row: interest = balance × r; principal = payment − interest; new balance follows.
- Fixed payments shift from interest-heavy to principal-heavy as the balance falls.
- Only the principal portion (plus extra principal) reduces what you owe.
- Spot-check month 1 whenever you generate a schedule so inputs are trustworthy.