Why amortization tables matter

A fixed-rate mortgage payment is constant, but the split between interest and principal changes every month. Early payments are mostly interest; later payments are mostly principal. Building the schedule from the standard formula makes that split auditable—useful when comparing lender quotes or checking a refinance break-even.

This note uses the usual U.S. fixed-rate, fully amortizing convention: monthly compounding, payment in arrears, no taxes/insurance in the payment (P&I only).

The payment formula

For principal $P$, annual note rate $r_{\text{annual}}$, and term of $n$ months:

\[ i = \frac{r_{\text{annual}}}{12}, \qquad M = P \cdot \frac{i(1+i)^{n}}{(1+i)^{n} - 1} \]

when $i > 0$. If $i = 0$, then $M = P / n$.

Worked example

Loan amount $320,000 (e.g. $400,000 price with 20% down), note rate 6.5%, term 30 years ($n = 360$).

P <- 320000
r_annual <- 0.065
n <- 360
i <- r_annual / 12

M <- P * i * (1 + i)^n / ((1 + i)^n - 1)
M

## [1] 2022.618

Monthly principal and interest is about $2022.62. Taxes, insurance, and HOA dues (if any) sit on top of this figure in a full PITI payment.

First twelve months

Each month:

Interest due $= \text{balance} \times i$
Principal paid $= M - \text{interest}$
New balance $= \text{balance} - \text{principal}$

balance <- P
rows <- vector("list", 12)
for (k in 1:12) {
  interest <- balance * i
  principal <- M - interest
  balance <- balance - principal
  rows[[k]] <- data.frame(
    month = k,
    payment = round(M, 2),
    interest = round(interest, 2),
    principal = round(principal, 2),
    balance = round(balance, 2)
  )
}
schedule <- do.call(rbind, rows)
knitr::kable(schedule, col.names = c(
  "Month", "Payment", "Interest", "Principal", "Ending balance"
))

Month	Payment	Interest	Principal	Ending balance
1	2022.62	1733.33	289.28	319710.7
2	2022.62	1731.77	290.85	319419.9
3	2022.62	1730.19	292.43	319127.4
4	2022.62	1728.61	294.01	318833.4
5	2022.62	1727.01	295.60	318537.8
6	2022.62	1725.41	297.20	318240.6
7	2022.62	1723.80	298.81	317941.8
8	2022.62	1722.18	300.43	317641.4
9	2022.62	1720.56	302.06	317339.3
10	2022.62	1718.92	303.70	317035.6
11	2022.62	1717.28	305.34	316730.3
12	2022.62	1715.62	307.00	316423.3

Interest in month 1 is much larger than principal. By month 12 the principal share has edged up, but the loan still has decades of amortization left.

Full-term totals (compact)

# Closed form for total interest over the life of the loan
total_paid <- M * n
total_interest <- total_paid - P
data.frame(
  months = n,
  monthly_PI = round(M, 2),
  total_paid = round(total_paid, 2),
  total_interest = round(total_interest, 2)
) |> knitr::kable()

months	monthly_PI	total_paid	total_interest
360	2022.62	728142.4	408142.4

Caveats

Lender quotes may use daily interest accruals, different day-count, or round pennies per period.
ARM loans, interest-only periods, and negative amortization need different schedules.
PMI, escrow, and points change cash due at closing and monthly, not the pure P&I formula above.
Confirm any decision that matters with the Loan Estimate / Closing Disclosure and a qualified advisor.

Mortgage amortization in R: payment formula and first-year schedule

AmortNotes

2026-10-28