Amortization Schedule With Daily Interest Calculator

This calculator estimates a level monthly payment and total interest for a loan using a monthly APR-based formula; it does not generate a true daily-interest amortization schedule. Enter the loan amount, APR, and term to see those estimates, then use the explanation below to understand why a lender’s daily accrual can produce different figures.

Formula

The calculator uses the standard fixed-payment formula for monthly compounding:

• Monthly rate: r = APR / 1200, expressed as a decimal per month.
• Number of payments: n = years × 12.
• Monthly payment: payment = principal × r / [1 − (1 + r)⁻ⁿ]. The displayed payment is rounded to cents.
• Estimated total interest: rounded monthly payment × n − principal.

Here, principal is the amount borrowed in dollars, APR is the annual percentage rate entered as a percentage, and years is the loan term in years. The formula assumes a fixed rate and equal monthly payments. It is not a daily-interest formula: it treats the monthly rate as APR divided by 12.

Worked Example

Using the calculator’s default inputs—$20,000, 8% APR, and 5 years—there are 5 × 12 = 60 monthly payments. The monthly rate is 8 / 1200 = 0.0066667.

Payment = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.

Estimated total interest = $405.53 × 60 − $20,000 = $4,331.80. This result uses the rounded monthly payment, as the calculator does. A lender’s actual schedule may differ because of daily accrual, payment dates, rounding, fees, or contract terms.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, monthly, and made at the end of each monthly period.
• Interest is represented by monthly compounding at APR divided by 12, not by a daily balance calculation.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

How Daily Interest Changes a Schedule

With daily accrual, interest is calculated for each day that a balance remains outstanding. A simple daily method commonly represents the daily rate as an annual rate divided by a day-count basis, such as 365; the actual contract determines the method and basis. Interest accrued over a period is then related to the outstanding principal and the number of elapsed days. Because months have different lengths and payment dates can vary, the interest portion of a payment may vary even when the required payment amount is level.

A typical schedule applies the payment first to interest accrued since the previous payment, then applies what remains to principal. The new principal balance becomes the starting point for the next accrual period. If a payment arrives later, more days may accrue before it is posted, potentially changing the interest charged and the remaining balance. The precise posting order and calculation depend on the loan agreement.

For a true daily schedule, you generally need the opening balance, annual rate, exact dates of each payment, payment amounts, day-count convention, and rules for posting payments. A schedule can be calculated day by day or over each interval between payments. This calculator lacks those inputs, so it cannot determine the exact daily accrual or reproduce a lender’s statement.

Reading and Using the Estimate

The monthly payment is a level-payment estimate, not necessarily the amount due under a particular contract. Total interest is the sum implied by that rounded payment over the stated term; it is not a payoff quote. The calculator is useful for seeing the relationship among principal, APR, and term under its stated assumptions, or for checking basic payment arithmetic.

To understand a specific loan, compare the estimate with the lender’s payment schedule and disclosure. Check whether the quoted APR is the rate the contract uses for accruing interest, whether payments are monthly, and whether the schedule includes charges or other amounts not represented here. For a daily-interest estimate, use the contract’s daily-rate convention and actual payment dates in a schedule that supports those details.

Common Differences and Misconceptions

• APR is not always the daily rate. This calculator divides APR by 12 for its monthly formula. A daily method may use a separate day-count convention specified by the contract.
• Daily interest does not necessarily mean daily payments. A loan may accrue interest each day while requiring payments monthly.
• Same payment does not mean same interest each period. Under daily accrual, the number of days between payments can vary, affecting the interest portion.
• Rounding matters. Payment rounding, daily interest rounding, and the timing of posting can create small differences that accumulate over a schedule.
• Extra or late payments change the path. Their effect depends on when they are credited and how the agreement applies them.

A common misconception is that a daily-interest loan must always cost more than a monthly-compounding estimate. There is no reliable conclusion from the label alone: the actual comparison depends on the rate definition, balance, dates, payment timing, and calculation rules. Use the contractual schedule for the actual amounts.

Frequently Asked Questions

How do I calculate daily interest on a loan?
Use the lender’s stated annual rate, day-count basis, current principal balance, and elapsed days. A simplified daily calculation multiplies the balance by the annual rate divided by the day-count basis and by the number of days. Contract rules may differ.

Can this calculator make a daily amortization schedule?
No. It estimates a monthly payment and total interest using APR divided by 12. A daily schedule requires dates, a daily accrual convention, payment amounts, and posting rules.

Does daily interest change my monthly payment?
It can affect interest accrued and the balance, but whether the required payment changes depends on the loan terms. Some schedules keep a required payment level while the interest and principal portions vary.

Why does my lender’s total interest differ from this result?
Possible causes include daily rather than monthly accrual, payment dates, rounding, fees, extra payments, or a different term or rate. Compare the inputs and assumptions with the lender’s disclosure.

Is APR divided by 365 always the daily rate?
No. The applicable day-count basis and rate calculation come from the loan terms. Do not assume a particular convention without checking the contract or asking the lender.

This 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