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An annuity schedule keeps the combined payment level; an equal-principal schedule keeps the principal portion level, so its total payment falls as interest declines. The TypeScript example below builds both schedules for the same principal, periodic rate, and term, making their cash flows directly comparable.
What an amortization schedule shows
An amortization schedule breaks each installment into interest and principal, then tracks the remaining balance. In a typical fixed-rate mortgage, the combined principal-and-interest payment stays substantially equal while the share going to interest falls and the share going to principal rises over time. See the CFPB explanation of how mortgage payments reduce a balance.
This example uses regular periods and a fixed rate. It models principal and interest only: it does not include taxes, insurance, fees, prepayments, or other contract terms.
How the two repayment methods differ
| Schedule feature | Annuity (equal payment) | Equal principal |
|---|---|---|
| Principal portion | Starts smaller and grows as the interest share shrinks. | Same each period. |
| Total installment | Level under fixed-rate, regular-period assumptions. | Starts higher and declines as interest falls. |
| Balance reduction | Principal reduction accelerates over time. | Balance falls by the same principal amount each period. |
| Typical tradeoff | More predictable installment amount. | Higher early installments and faster early balance reduction. |
| Total interest | Generally higher than equal principal for the same principal, positive fixed rate, and term. | Generally lower under those matched assumptions. |
These are consequences of the stated model, not universal promises about loan contracts. Oracle describes equal-principal repayment as equal principal across installments with variable interest and a varying total payment in its Oracle Loans User Guide.
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Define the inputs and formulas
Let P be starting principal, n the number of payment periods, and r the rate per period. The code expects r as a decimal, so 0.05 means 5% per period; 5 means 500% per period. It does not convert an annual rate. If the input is annual, first choose the payment frequency and whether the quoted rate is nominal or effective, then convert it consistently to a per-period rate.
Annuity payment
For nonzero r, the level payment is P × r / (1 − (1 + r)−n). For zero interest, it is P / n. Each period, interest is opening balance times r; principal is payment minus interest; closing balance is opening balance minus principal.
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Equal-principal payment
Scheduled principal is P / n each period. Interest is opening balance times r, and total payment is scheduled principal plus interest. With a positive fixed rate, the declining opening balance makes the interest and total payment decline.
Build both schedules in TypeScript
This teaching implementation retains unrounded values through the recurrence and rounds only when formatting output. It accepts finite, nonnegative principal, a positive integer term, and a finite, nonnegative periodic rate. Negative rates are deliberately not supported. The last row uses the remaining balance as its principal amount to close the schedule without a floating-point residue.
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type ScheduleRow = {
period: number;
openingBalance: number;
payment: number;
interest: number;
principal: number;
closingBalance: number;
};
type Method = "annuity" | "equalPrincipal";
function buildSchedule(
principal: number,
periodicRate: number,
periods: number,
method: Method,
): ScheduleRow[] {
if (!Number.isFinite(principal) || principal < 0) {
throw new RangeError("principal must be finite and nonnegative");
}
if (!Number.isFinite(periodicRate) || periodicRate < 0) {
throw new RangeError("periodicRate must be finite and nonnegative");
}
if (!Number.isInteger(periods) || periods <= 0) {
throw new RangeError("periods must be a positive integer");
}
const levelPayment = periodicRate === 0
? principal / periods
: principal * periodicRate /
(1 - Math.pow(1 + periodicRate, -periods));
const scheduledPrincipal = principal / periods;
let balance = principal;
const rows: ScheduleRow[] = [];
for (let period = 1; period <= periods; period++) {
const openingBalance = balance;
const interest = openingBalance * periodicRate;
const isFinal = period === periods;
let payment: number;
let principalPaid: number;
let closingBalance: number;
if (method === "annuity") {
// Clear any accumulated floating-point residue in the final period.
principalPaid = isFinal ? openingBalance : levelPayment - interest;
payment = principalPaid + interest;
closingBalance = isFinal ? 0 : openingBalance - principalPaid;
} else {
principalPaid = isFinal ? openingBalance : scheduledPrincipal;
payment = principalPaid + interest;
closingBalance = isFinal ? 0 : openingBalance - principalPaid;
}
rows.push({
period,
openingBalance,
payment,
interest,
principal: principalPaid,
closingBalance,
});
balance = closingBalance;
}
return rows;
}
const annuity = buildSchedule(1000, 0.01, 3, "annuity");
const equalPrincipal = buildSchedule(1000, 0.01, 3, "equalPrincipal");
// Presentation only: this is not a lender's posting or rounding policy.
const display = (rows: ScheduleRow[]) =>
rows.map(row => ({
...row,
openingBalance: Number(row.openingBalance.toFixed(2)),
payment: Number(row.payment.toFixed(2)),
interest: Number(row.interest.toFixed(2)),
principal: Number(row.principal.toFixed(2)),
closingBalance: Number(row.closingBalance.toFixed(2)),
}));The checks reject invalid inputs before calculation. A zero principal is allowed and produces zero-valued rows. Since the function takes a rate per period, its term is also a count of those same periods; for example, monthly periods require a monthly rate and a number of months.
Compare the resulting cash flows
With principal 1,000, a rate of 1% per period, and three periods, the unrounded model produces the following values. The table shows currency-style values rounded to two decimals for readability; this display rounding is not applied inside the recurrence.
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| Method | Period | Opening balance | Payment | Interest | Principal | Closing balance |
|---|---|---|---|---|---|---|
| Annuity | 1 | 1,000.00 | 340.02 | 10.00 | 330.02 | 669.98 |
| Annuity | 2 | 669.98 | 340.02 | 6.70 | 333.32 | 336.66 |
| Annuity | 3 | 336.66 | 340.03 | 3.37 | 336.66 | 0.00 |
| Equal principal | 1 | 1,000.00 | 343.33 | 10.00 | 333.33 | 666.67 |
| Equal principal | 2 | 666.67 | 340.00 | 6.67 | 333.33 | 333.33 |
| Equal principal | 3 | 333.33 | 336.67 | 3.33 | 333.33 | 0.00 |
The final annuity installment is adjusted to clear the balance; its displayed value differs by a cent from the earlier installments. Totals computed from unrounded values are about 20.10 in interest for annuity and 20.00 for equal principal. Rounded row values may not sum exactly to an unrounded total.
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Choose and document a currency-rounding policy
TypeScript’s number is JavaScript Number behavior, which uses double-precision binary floating point; it is not exact decimal currency arithmetic. The TypeScript Handbook describes the number and bigint types, and the ECMAScript Number specification defines Number representation. Formatting with toFixed(2) is a display choice, not proof that a lender would post those amounts.
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This example does not round each period. A real contract may instead calculate or post rounded amounts period by period and handle the final installment according to its own rules. Production software should follow the applicable contract and jurisdiction; integer minor units or decimal arithmetic may be more suitable than ordinary floating-point calculations. Do not switch to per-period rounding without also specifying how interest, principal, and any final adjustment are posted.
What the example does not model
A mathematically regular schedule may not match a real account statement. Actual loans can use different payment dates, day-count conventions, irregular first or last periods, fees, rate changes, or prepayments. Those details affect calculations; the CFPB notes that odd periods and schedule irregularities can cause minor variations in otherwise substantially equal payments in its 2024 edition of 12 CFR § 1026.43.
The same regulation gives a rounded example of a $200,000, 30-year fixed-rate loan at 7 percent with a substantially equal monthly fully amortizing payment of $1,331, calculated using non-rounded values. It is a regulatory illustration, not a current quote or a general promise of what a borrower will pay.
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