Quarterly Amortization Schedule Calculator

A quarterly amortization schedule shows how a loan balance changes after each three-month payment, separating each payment into interest and principal. Enter the loan amount, annual interest rate, and term to calculate the quarterly payment and total interest; the schedule itself can be built from those figures using the steps below.

Formula

This calculator uses the standard fixed-rate, level-payment loan formula on a monthly basis. It does not produce a quarterly schedule directly; its results illustrate the monthly calculation. For an actual quarterly schedule, use the quarterly formula and make one payment every three months.

For quarterly payments, the payment is A = P × i / [1 − (1 + i)⁻ⁿ], where P is the original principal in dollars, i is the interest rate per quarter as a decimal, n is the number of quarterly payments, and A is the payment in dollars. If the quoted nominal annual rate is compounded quarterly, then i = annual rate / 4 and n = years × 4. The corresponding monthly formula used by this calculator is M = P × r / [1 − (1 + r)^−N], where r = APR / 1200, N = years × 12, and M is the monthly payment. The calculator rounds M to cents.

For either schedule, each period follows three steps: interest = opening balance × periodic rate; principal repaid = payment − interest; closing balance = opening balance − principal repaid. The next period starts with the previous closing balance. The final payment can differ slightly because of cent rounding or a lender’s payoff calculation.

Worked Example

Using the calculator’s default monthly inputs—$20,000 principal, 8% APR, and a five-year term—r = 0.08 / 12 = 0.0066667 and N = 5 × 12 = 60.

M = 20,000 × 0.0066667 / [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53 per month after rounding to cents. Total of scheduled payments is $405.53 × 60 = $24,331.80; total interest is $24,331.80 − $20,000 = $4,331.80.

For comparison, if the same $20,000 were repaid over five years with quarterly payments and a nominal 8% rate compounded quarterly, i = 0.08 / 4 = 0.02 and n = 5 × 4 = 20. The quarterly payment would be 20,000 × 0.02 / [1 − (1.02)⁻²⁰] = approximately $1,223.08. This is an illustrative quarterly calculation, not the calculator’s monthly output. Its final payment and total can vary by a few cents if each installment is rounded.

How a Quarterly Amortization Schedule Works

A schedule is a period-by-period ledger, not just a payment estimate. For the quarterly example, the first quarter’s interest is $20,000 × 2% = $400. Of the approximately $1,223.08 payment, about $823.08 reduces principal, leaving a balance near $19,176.92. In the next quarter, interest is calculated on that lower balance: about $383.54. The payment stays level, but its interest portion generally declines as the principal portion grows.

A schedule commonly includes payment number or date, opening balance, payment amount, interest, principal, and closing balance. A simple way to construct it is:

1. Set the opening balance for period one to the original principal.
2. Calculate that period’s interest using the opening balance and periodic rate.
3. Subtract interest from the scheduled payment to find principal repaid.
4. Subtract principal repaid from the opening balance to find the closing balance.
5. Repeat with the closing balance as the next opening balance, adjusting the last payment if needed to clear the debt.

Choosing the Correct Payment Period

“Quarterly” means once every three months, usually four scheduled payments per year. It is not the same as paying monthly and grouping four payments into a quarterly summary. A loan may accrue interest monthly, daily, or under another contract convention even when installments are quarterly. The schedule must follow the contract’s accrual method and payment dates; simply dividing an APR by four is appropriate only when the quoted rate and compounding convention support that conversion.

Check whether the stated annual rate is nominal or effective. A nominal annual rate compounded quarterly is divided by four to obtain the quarterly periodic rate. An effective annual rate instead converts to a quarterly rate as (1 + effective annual rate)^1/4 − 1. Mixing these definitions changes the payment and total interest. Use the lender’s stated periodic rate or its disclosed calculation method when available.

Reading the Results and Their Limits

The payment answers how much is due each period under the assumptions; total interest estimates the interest across all scheduled payments. A larger principal or longer term generally changes both figures, but the exact result depends on rate, payment frequency, rounding, and the contract’s accrual rules. The monthly calculator’s output should not be read as the quarterly installment: to estimate quarterly payments, use quarterly inputs and a quarterly formula.

These formulas assume a fixed rate and equal payments. They do not model variable-rate resets, irregular first periods, grace periods, balloon payments, deferred interest, missed installments, prepayment penalties, or extra principal payments. Fees, taxes, insurance, and escrow are not included. An amortization schedule is therefore a mathematical estimate, not a statement of the amount due on a particular date.

Common Errors When Building a Schedule

• Using the annual rate as the period rate: Convert the rate to the applicable month or quarter before calculating interest.
• Using the wrong number of payments: A five-year quarterly schedule has 20 periods; a five-year monthly schedule has 60.
• Applying interest to the original loan every period: For an amortizing loan, calculate each period’s interest on its opening balance.
• Rounding too early: Keep enough precision internally, then round displayed money to cents according to the lender’s method. Repeated rounding can leave a small residual balance.
• Assuming every quarterly payment is a lumped group of monthly payments: Timing and interest accrual are different, so the results need not match.

Assumptions

• Fixed rate and equal scheduled payments; the example uses the calculator’s monthly formula, while the comparison uses quarterly compounding.
• Payments are made at the end of each period, after that period’s interest accrues.
• Monthly compounding is APR / 12 in the calculator; the illustrative quarterly calculation uses the nominal rate divided by four.
• Fees, taxes, insurance, PMI, and escrow are not included.

Frequently Asked Questions

What does a quarterly amortization schedule show?
It shows each quarter’s opening balance, payment, interest, principal reduction, and ending balance. It also makes the gradual change in the interest and principal portions visible.

How do I calculate a quarterly loan payment?
Convert the annual rate to a quarterly rate under the loan’s compounding convention, multiply the loan term in years by four for the number of payments, then apply A = P × i / [1 − (1 + i)⁻ⁿ].

Is a quarterly payment one-fourth of the annual payment?
Not necessarily. Loan payments are calculated from the periodic rate and number of periods. A quarterly installment is not generally equal to three monthly installments because balances and interest accrue on different dates.

Why does the last payment differ from the others?
Cent rounding, payment-date timing, or the lender’s payoff calculation can leave a small remaining balance. The final amount is often adjusted to bring the balance to zero.

Can I use this calculator for a quarterly loan?
This calculator’s specified outputs are monthly payment and total interest based on monthly periods. Use the quarterly formula and the contract’s rate convention for a quarterly schedule; obtain the actual payment terms from the lender.

The result is an estimate, and the lender’s disclosure gives the exact figures.

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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 | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2