How the compound-interest loan math works

A “compound interest loan” means interest is calculated on your outstanding balance, added on a schedule, and then future interest is calculated on that new (slightly larger) balance. That’s the compounding effect. Many everyday loans feel “simple” because you see one fixed monthly payment, but under the hood the lender is running a repeatable loop each period: compute interest, apply your payment, reduce the balance, repeat. This calculator exposes that loop so you can plan, compare, and share the results clearly.

The important nuance is that compounding frequency and payment frequency can be different. For example, interest might accrue (and be added) daily, while you only make a payment monthly. When that happens, the effective monthly interest rate is a bit higher than APR/12 because interest has had more opportunities to build up before you pay it down. That difference is usually small on a single month — but on long terms, high balances, or high APRs, it becomes noticeable.

Principal (P) is the amount you borrow. APR is the annual rate your lender discloses. A common oversimplification is “monthly rate = APR/12,” but that assumes monthly compounding and monthly payments. If the loan compounds m times per year, the nominal rate per compounding step is: i = APR / m.

If you pay p times per year (monthly = 12, biweekly = 26, weekly = 52), we compute the effective rate per payment period: r = (1 + APR/m)^m/p − 1. This conversion is what lets you compare “daily compounding + monthly payment” against “monthly compounding + monthly payment” in a consistent way.

For a fixed-rate, fully amortizing loan, the classic payment formula is: Payment = P × r / (1 − (1 + r)⁻ⁿ), where n is the total number of payments (termYears × p). This creates a payment that — in theory — takes the balance to zero at the end of the term.

Each period then follows the same split:

• Interest = Balance × r
• Principal = Payment − Interest
• New balance = Balance − Principal

Interest-only means you cover interest but do not reduce principal. The balance stays nearly the same, so the payment is roughly Balance × r each period. This is common in certain bridge loans or specialty products. No payments is the pure compound-interest case: your balance grows by compounding, with no reduction. The future value after t years is: Future balance = P × (1 + APR/m)^m×t.

Extra payments reduce principal faster. Because interest is computed on the remaining balance, reducing balance earlier reduces interest for every period after that. That’s why even a small extra payment can create an outsized effect over time — especially on long terms. This calculator treats the extra amount as principal reduction (the most common behavior), but always confirm how your lender applies extra payments in your specific contract.

Omni-style reminder: Real-world schedules can differ slightly due to lender-specific rounding rules, payment posting dates, day-count conventions (actual/365 vs 30/360), and fees. Use this as a high-quality estimate and comparison tool.

Examples you can screenshot and share

The easiest way to use this page (and the easiest way to make it “viral” in a helpful way) is to run two or three scenarios and compare the “Total Interest” number. People don’t argue with a screenshot that shows “You paid $X in interest.”

Example A: Auto loan baseline vs extra payment

• Loan amount: $25,000, APR: 8.5%, Term: 5 years
• Set compounding to Monthly and payment frequency to Monthly
• Calculate, then set extra payment = $50 and calculate again
• Save both scenarios to compare later

Example B: Daily compounding “interest shock”

• Loan amount: $5,000, APR: 19.99%, Term: 2 years
• Compounding: Daily, Payments: Monthly
• Now switch compounding to Monthly and compare total interest

Example C: Biweekly payments

• Use the same loan as Example A
• Change payment frequency from Monthly to Biweekly
• Many people notice a lower total interest because principal falls faster

Sharing idea: Post a “before vs after” screenshot: “Same loan, +$50 extra per payment → saved $____ interest.” It’s practical, not gimmicky, and it tends to spread because it helps people.

How to use this calculator like a finance pro

The biggest mistake people make with loan calculators is treating them as a one-and-done answer. The real power is scenario planning: “If I pay $25 extra, what happens?” “If I refinance from 9.5% to 7.5%, what changes?” “Is biweekly worth it?” The interface on this page is designed to make those comparisons fast.

• APR: Use the disclosed APR. If fees are rolled into the loan, add them to the principal.
• Compounding: If unsure, choose Monthly for most installment loans; choose Daily for credit-style products.
• Payment frequency: Choose how you actually pay (monthly, biweekly, weekly).

The mini schedule shows the first 12 periods. Early on, your balance is highest, so the interest portion is largest. That’s why it can feel like “I’m paying but the balance barely moves.” Over time, as the balance shrinks, interest shrinks, and more of each payment hits principal. If you want to accelerate that transition, extra payments are the cleanest lever.

The meter is a quick visual of how painful the interest is relative to the amount borrowed. A 10-year term at moderate APR might create a high ratio even if the monthly payment feels “comfortable.” That’s the tradeoff: lower payment often means more total interest.

Click Save Scenario after each calculation. Then click a saved scenario to reload it instantly. This is perfect for building a small “decision set” (baseline, extra payment, refinance rate, biweekly).

• Variable rates (ARM/adjustable products)
• Grace periods, deferment, or special capitalization events
• Lender-specific posting rules and exact calendars beyond the preview

If you want an “Omni-level” workflow: run your baseline, run a “+extra payment” scenario, and run a “refinance rate” scenario. Compare total interest and payoff time. Pick the option that matches your cashflow and goals.

Frequently Asked Questions

• Why is my calculated payment different from my lender’s?

  Small differences usually come from rounding, fees, day-count conventions, or how the lender defines “payment period.” Some lenders compound daily but quote a payment that assumes a specific posting schedule. Use this calculator for planning, and treat lender documents as the official numbers.

• What if my APR is 0%?

  Then the payment is simply principal divided by number of payments. The schedule becomes pure principal repayment. This calculator supports 0% APR.

• Is “biweekly” always better than monthly?

  Often it reduces interest because you pay down principal sooner, and you may effectively make one extra monthly payment per year. But it depends on whether your lender applies each biweekly payment immediately or holds it until a monthly due date.

• Does extra payment reduce the monthly payment?

  Typically it reduces payoff time (and total interest), not the scheduled payment. Some lenders will “recast” the loan (rare on consumer loans) which can reduce payments. This calculator assumes you keep the scheduled payment and pay off faster.

• Is this the same as a compound interest savings calculator?

  The compounding math is similar, but loans involve payments that reduce principal. Savings calculators usually assume you’re adding contributions. Here, your payments fight against interest, and the schedule shows how that battle plays out.