Amortization Table With Quarterly Payments

A quarterly-payment amortization table shows how each payment is divided between interest and principal, and how the balance changes after every three-month payment period. Enter the loan amount, annual APR, and term in years to calculate the regular quarterly payment and total interest; the table itself can then be built by applying the same balance calculation period by period.

Formula

For a fixed-rate loan with equal payments at the end of each quarter, the payment is calculated using the level-payment amortization formula:

Payment = P × r / [1 − (1 + r)^−N]

• P is the amount borrowed, in dollars.
• r is the quarterly interest rate as a decimal: annual APR ÷ 400. For an 8% APR, r = 8 ÷ 400 = 0.02, or 2% per quarter.
• N is the number of quarterly payments: loan term in years × 4.

Total interest in this estimate is the rounded quarterly payment multiplied by the number of payments, minus the original principal: Total interest = payment × N − P. The calculator rounds the payment to cents before calculating this total, so it reflects a schedule of equal cent-rounded payments. A real lender may adjust the final payment to clear a small remaining balance.

Worked Example

Using the calculator’s defaults, the loan is $20,000 at 8% annual APR for 5 years. There are 5 × 4 = 20 quarterly payments, and the quarterly rate is 8% ÷ 400 = 0.02.

1. Payment = 20,000 × 0.02 ÷ [1 − (1.02)⁻²⁰].
2. (1.02)⁻²⁰ is approximately 0.672971.
3. Payment = 400 ÷ (1 − 0.672971) = 400 ÷ 0.327029, or approximately $1,223.14 when rounded to cents.
4. Total interest = $1,223.14 × 20 − $20,000 = $4,462.80.

These are the calculator’s results for those inputs: a quarterly payment of $1,223.14 and estimated total interest of $4,462.80.

Assumptions

• The APR stays fixed throughout the stated term.
• Payments are equal, made at the end of each quarter, with the first payment one quarter after the loan begins.
• Interest accrues quarterly at APR ÷ 4. This is a periodic-rate calculation, not a daily-interest calculation.
• The estimate excludes fees, taxes, insurance, PMI, and escrow because none are calculator inputs.

How to Build and Read the Table

The payment formula gives the regular amount, but the amortization table reveals what happens inside each payment. For every quarter, calculate interest on the balance at the start of that period, subtract that interest from the payment to find principal repaid, then subtract the principal portion from the starting balance.

1. Beginning balance: Use the original loan amount for the first quarter. For later quarters, use the previous quarter’s ending balance.
2. Quarterly interest: Beginning balance × quarterly rate.
3. Principal paid: Quarterly payment − interest for that quarter.
4. Ending balance: Beginning balance − principal paid.

For the example, first-quarter interest is $20,000 × 0.02 = $400. The principal portion is $1,223.14 − $400 = $823.14, leaving an ending balance of $19,176.86. In the second quarter, interest is approximately $19,176.86 × 0.02 = $383.54. The payment stays the same, so about $839.60 goes to principal and the balance falls to approximately $18,337.26. Small differences can occur from rounding intermediate amounts.

A typical table has columns for payment number or date, beginning balance, payment, interest, principal, and ending balance. Early payments generally allocate a larger share to interest because the outstanding balance is larger. As principal is paid down, interest per quarter declines and more of the fixed payment goes toward principal. The balance should reach zero after the scheduled final payment, apart from rounding or lender-specific adjustments.

When Quarterly Payments Apply

Quarterly schedules mean four payments per year, rather than monthly payments. They may appear in business, commercial, or other loan arrangements, but the contract determines the actual frequency, due dates, rate convention, and payment amount. Do not assume that a quoted annual rate is applied as APR divided by four: a lender may calculate interest using daily balances or another stated convention. Use the contract’s payment schedule and calculation method for an exact reconciliation.

Changing payment frequency also changes the number and timing of payments. For the same annual APR and term, this calculator uses four periods per year and APR ÷ 4. It does not simply take a monthly payment and multiply it by three; the quarterly payment is recalculated with a quarterly rate and a different number of periods.

Common Errors and Limits

• Confusing quarterly with monthly: Use four periods per year, so a five-year term has 20 payments, not 60.
• Using APR as a decimal incorrectly: The calculator accepts APR as a percent, such as 8, and converts it with APR ÷ 400. Do not enter 0.08 for 8%.
• Assuming total interest includes every borrowing cost: It includes only modeled interest less principal. Fees and other charges are not included.
• Expecting every lender’s final balance to match exactly: Rounding, payment dates, daily accrual, and the lender’s stated rate method can change individual entries or the final payment.

This standard formula assumes a positive fixed APR and equal end-of-quarter payments. It does not model variable rates, irregular first periods, extra payments, skipped payments, balloon payments, or a changing schedule. For those cases, the payment and each period’s interest must be calculated using the loan’s actual terms. Obtain the APR, fee treatment, payment dates, and interest convention from the lender’s disclosure rather than treating the example defaults as quoted terms.

Frequently Asked Questions

How do you calculate a quarterly loan payment?
Convert the APR to a quarterly decimal rate by dividing the percentage APR by 400. Multiply the loan amount by that rate, then divide by 1 minus (1 + rate) raised to the negative number of quarterly payments.

How many quarterly payments are in a five-year loan?
There are 20 scheduled payments: five years × four quarters per year. The actual due dates are set by the loan agreement.

Is a quarterly payment three times the monthly payment?
No. The payment is recalculated using the quarterly rate and the total number of quarterly periods. Multiplying a monthly payment by three generally does not reproduce the quarterly amortization schedule.

Why does the interest portion fall over time?
Each period’s interest is calculated on the remaining balance. As payments reduce that balance, the interest amount declines, leaving more of an unchanged payment to repay principal.

Does the table include fees or taxes?
No. This calculation models principal and interest only. Review the lender’s written figures for fees, taxes, insurance, escrow, or other charges that may apply to a particular loan.

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

Related

• Variable Rate Loan Amortization Table Calculator
• Home Loan Amortization Table: Payments and Balance
• House Amortization Table: Monthly Payment and Balance

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 | $ | p * (apr / 400) / (1 - (1 + apr / 400) ^ -(yrs * 4)) | 2
out int | Total interest | $ | pmt * yrs * 4 - p | 2