Quarterly Amortization Table: Payments and Balance

A quarterly amortization table shows how each scheduled payment is divided between interest and principal, and how the loan balance changes after every three-month payment period. Enter the loan amount, annual interest rate, and term below to calculate a level quarterly payment, total interest, and total paid; the outputs are summaries, not a period-by-period table.

Formula

For a fixed-rate loan with equal payments made every quarter, the payment is calculated using the standard level-payment formula:

PMT = round[P × r / (1 − (1 + r)⁻ⁿ), 2]

• PMT is the quarterly payment, in dollars.
• P is the starting loan principal, in dollars.
• r is the quarterly interest rate as a decimal: APR ÷ 400. This assumes a quoted annual percentage rate is divided evenly across four quarters.
• n is the number of quarterly payments: term in years × 4.

The calculator rounds each scheduled payment to the nearest cent, then calculates total payments as PMT × n and total interest as total payments − P. This makes the totals consistent with the displayed payment. A lender may handle the final payment differently to clear a small balance caused by cent rounding.

Worked Example

Using the calculator’s defaults: principal $20,000, APR 8%, and a five-year term.

1. Convert the annual rate to a quarterly decimal: 8 ÷ 400 = 0.02, or 2% per quarter.
2. Count the payments: 5 × 4 = 20 quarters.
3. Apply the payment formula: $20,000 × 0.02 ÷ [1 − (1.02)⁻²⁰] = about $1,223.91 per quarter, rounded to cents.
4. Total payments using the rounded payment: $1,223.91 × 20 = $24,478.20.
5. Total interest: $24,478.20 − $20,000 = $4,478.20.

The payment is an estimate under the stated assumptions. The calculator summarizes totals; a full amortization table would show the interest, principal, and remaining balance for each of the 20 quarters.

Assumptions

• The interest rate remains fixed for the full term.
• Payments are equal, made at the end of each three-month period, with the first payment after one quarter.
• Interest accrues at the APR divided by four for each quarter. This is a periodic-rate approximation; a contract may define accrual using actual days or another convention.
• Fees, taxes, insurance, escrow, and other charges are not included.

How to Read a Quarterly Amortization Table

A complete table usually has one row per payment period. Its columns commonly include the payment number or date, opening balance, payment amount, interest portion, principal portion, and closing balance. At the start, interest generally makes up a larger share of a level payment because the outstanding balance is larger. As principal is repaid, the interest portion typically declines and more of each payment reduces principal.

For a period with opening balance B and quarterly rate r, a simple schedule calculates interest as B × r, then principal repaid as payment − interest. The new balance is opening balance − principal repaid. For example, in the first quarter of the default example, estimated interest is $20,000 × 0.02 = $400. The approximate principal reduction is $1,223.91 − $400 = $823.91, leaving about $19,176.09. A lender’s exact schedule can differ because of payment dates, rounding, and the contract’s interest method.

When Quarterly Payments Apply

Quarterly payment frequency means one payment every three months, or four scheduled payments per year. It is distinct from monthly repayment, even when both loans have the same annual rate and term. With quarterly payments, interest and principal are generally settled less often, and the payment amount is larger than a comparable monthly installment. Do not enter a quarterly rate as though it were an annual APR: this calculator expects an annual rate and converts it by dividing by four.

The input range allows loan terms in years, but the formula treats the term as a whole number of quarters by multiplying years by four. Because a fraction of a year can produce a fractional number of quarters, use a term that reflects the actual count of scheduled payments. For a contract with irregular first or final periods, a simple equal-quarter model may not match its schedule.

Common Errors and Limits

• Confusing APR and periodic rate: Enter the annual percentage rate as a percent, such as 8, not 0.08 and not the quarterly rate of 2.
• Assuming every lender uses identical accrual: Some contracts calculate interest based on days elapsed or other terms rather than a fixed APR/4 period. Use the lender’s schedule for the contractual figures.
• Expecting every row to be identical to a forecast: Payment dates, skipped or late payments, rate changes, and extra principal payments can change the allocation and remaining balance.
• Reading total interest as a complete borrowing cost: The estimate includes only modeled interest. Fees and other charges are outside the calculation.
• Ignoring rounding: Each payment is rounded to cents here. Repeated rounding can leave a small difference in the final payment; the lender may adjust that last amount.

The calculator also does not model variable rates, payment holidays, balloon payments, amortization schedules with uneven periods, or extra payments. For a full table, calculate each quarter’s interest and principal from that period’s opening balance, then carry the resulting closing balance into the next row.

Frequently Asked Questions

What does a quarterly amortization table show?
It lists each three-month payment period and typically separates the payment into interest and principal while showing the loan balance before and after the payment.

How many payments are in a five-year quarterly loan?
A five-year term with four payments per year has 20 scheduled quarterly payments.

Is a quarterly payment the same as a monthly payment?
No. A quarterly payment is made once every three months, while monthly payments are made 12 times per year. Payment size and the timing of principal reduction differ.

How do I calculate interest in one quarter?
Under the fixed periodic-rate assumption, multiply the opening balance by the quarterly rate. If the APR is 8%, the modeled quarterly rate is 8% ÷ 4 = 2%.

Why does my lender’s schedule show different amounts?
It may use exact payment dates, a different interest-accrual convention, fees, a different rounding method, or contract-specific payment terms. Compare the assumptions and use the lender’s disclosure for the official figures.

This result is an estimate for educational purposes, and the lender’s disclosure gives the exact figures.

Related

• Amortization Table for Notes Receivable
• Real Estate Amortization Table: Payments and Balance
• Loan Amortization Factors Table: Formula and Calculator

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Quarterly payment | $ | round(p * (apr / 400) / (1 - (1 + apr / 400) ^ -(yrs * 4)), 2) | 2
out int | Total interest | $ | pmt * yrs * 4 - p | 2
out tot | Total payments | $ | pmt * yrs * 4 | 2