Formula
Payment = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n − 1 ]
No separate source: the formula follows by arithmetic from the steps below, each with its own basis.
- P
- Loan principal.
- r
- Periodic interest rate: the annual rate divided by 12 for monthly payments.
- n
- Total number of payments in the amortization period, not the loan term.
Where the formula comes from
As this course defines it, the payment is the same amount in every period, and the schedule repays the loan in full with the last of its n payments: the balance after payment n is zero.
The course's own definition: it cites no published source.
As this course defines it, each payment consists of principal and interest.
The course's own definition: it cites no published source.
The interest in each payment is one period's interest on the balance before it, at the periodic rate r, and the rest repays principal. So the balance after payment k is Bₖ = Bₖ₋₁ × (1 + r) − Payment, starting from B₀ = P.
Arithmetic on the steps above.
Applying that n times and summing the geometric series gives Bₙ = P × (1 + r)^n − Payment × [ (1 + r)^n − 1 ] ÷ r.
Arithmetic on the steps above.
Setting Bₙ to zero, as step 1 requires, and solving for the payment gives Payment = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n − 1 ].
Arithmetic on the steps above.
How it works
The distinction that matters most in commercial lending is between the amortization period and the loan term. A residential mortgage typically has a 30-year term and a 30-year amortization, so it pays itself off. A commercial mortgage commonly has a 10-year term and a 30-year amortization: payments are calculated as if the loan will take 30 years to repay, but the entire remaining balance falls due at year 10. The amortization period sets the payment; the term sets the deadline.
Every payment splits between interest and principal, and the split shifts over time. Early payments are almost entirely interest, because interest accrues on a large outstanding balance. As principal is repaid the interest portion shrinks and the principal portion grows, which is why the balance declines slowly at first and then accelerates. On a 30-year schedule, roughly 15% of the original principal has been repaid after ten years.
Lengthening the amortization period is the most direct way to improve DSCR without changing the interest rate or the loan amount. A longer schedule spreads principal over more payments, lowering the annual debt service that sits in the DSCR denominator. This is why a borrower who fails a coverage test will often ask for 30-year amortization rather than 25, and why lenders treat amortization as a credit term, not an administrative detail.
The cost of that relief is slower deleveraging. A loan on a 30-year schedule leaves a much larger balance outstanding at maturity than one on 20 years, which means more refinancing risk. If values or income have fallen by the time the balloon arrives, the borrower must refinance a larger balance against a weaker asset.
Worked example
A $6,000,000 loan at 6.5% interest. Compare a 25-year amortization with a 30-year, both on a 10-year term.
| Step | Calculation | Result |
|---|---|---|
| Monthly payment, 25-year schedule | $6,000,000 at 6.5% over 300 months | $40,512 |
| Monthly payment, 30-year schedule | $6,000,000 at 6.5% over 360 months | $37,924 |
| Annual debt service difference | ($40,512 − $37,924) × 12 | $31,060 |
| DSCR at each, on $600,000 NOI | $600,000 ÷ $486,024 vs $600,000 ÷ $455,088 | 1.234x vs 1.318x |
| Balance remaining at year 10 | 25-year schedule vs 30-year schedule | $4,651,000 vs $5,087,000 |
Five extra years of amortization lifts DSCR from 1.234x to 1.318x, enough to move a deal from failing a 1.25x test to passing it comfortably, with no change in rate or loan amount. The cost appears at maturity: the borrower owes $436,000 more at the balloon. Amortization does not reduce debt; it postpones it.
How it compares
| Structure | Effect on payment | Effect on balloon balance |
|---|---|---|
| Interest-only | Lowest payment | Full original principal due at maturity |
| 30-year amortization | Low payment | Roughly 85% of principal still outstanding at year 10 |
| 25-year amortization | Moderate payment | Roughly 78% outstanding at year 10 |
| 20-year amortization | High payment | Roughly 66% outstanding at year 10 |
| Fully amortizing over the term | Highest payment | Nothing due at maturity |
Common mistakes
- Confusing the amortization period with the loan term
- A 10-year term on a 30-year schedule does not repay the loan. The balance is due in ten years, and refinancing it is the borrower's problem.
- Assuming half the loan is repaid halfway through the schedule
- Amortization is not linear. After 15 years of a 30-year schedule, roughly 27% of principal has been repaid, not 50%.
- Underwriting DSCR on an interest-only payment for a loan that later amortizes
- Coverage will fall the moment amortization begins, and most lenders test the amortizing payment from the outset for exactly that reason.
Frequently asked questions
- What is the difference between loan term and amortization period?
- The amortization period is the schedule used to calculate the payment; the loan term is how long the loan actually lasts before the balance is due. A commercial mortgage with a 10-year term and 30-year amortization is paid as though it will take 30 years to repay, but the entire remaining balance becomes payable at year 10.
- Why do commercial loans use a longer amortization than term?
- Because a longer amortization produces a smaller payment, which improves debt service coverage and therefore supports a larger loan. Lenders limit their own exposure by keeping the term short, so they can reprice or exit at maturity.
- How much principal is repaid over a 10-year term on 30-year amortization?
- Roughly 15% of the original loan amount, because early payments are weighted heavily toward interest. Around 85% of the principal remains outstanding as a balloon payment at maturity.