Calculate Loan Interest on a Reducing Balance

This calculator estimates the monthly payment and total interest for a fixed-rate, reducing-balance loan from its amount, annual APR, and term. Enter those three figures to see the payment and the interest implied by the calculator’s rounded monthly payments.

Formula

For equal monthly payments on a fixed-rate loan, the payment is calculated using the standard amortizing-loan formula:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100. With APR entered as a percentage, r = APR ÷ 1200.
• n is the number of monthly payments: loan term in years × 12.
• Payment is the scheduled monthly payment, in dollars.

The calculator rounds the payment to cents. It estimates total interest as (rounded monthly payment × n) − P. This is a convenient estimate based on the displayed payment; a lender’s final payment schedule may differ because of payment-date conventions, rounding, fees, or a small adjustment to the last payment.

Worked Example

Using the calculator’s default values—$20,000 borrowed, 8% APR, and 5 years:

1. Convert the annual percentage rate to a monthly decimal: r = 8 ÷ 1200 = 0.0066667.
2. Find the number of monthly payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.
4. Calculate estimated total interest using that rounded payment: ($405.53 × 60) − $20,000 = $4,331.80.

The calculator therefore displays a monthly payment of $405.53 and estimated total interest of $4,331.80.

Assumptions

• The interest rate is fixed for the full term.
• There are equal monthly payments, made at the end of each monthly period.
• Interest accrues monthly using APR divided by 12; this calculation does not model daily interest or a lender’s specific day-count method.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

How Reducing-Balance Interest Works

With a reducing-balance loan, interest for a period is calculated on the outstanding principal—not on the original amount for the entire term. A scheduled payment covers that period’s interest first; the remainder reduces principal. As the balance falls, the interest portion generally falls too, while the principal portion grows, provided the payment and rate remain unchanged.

For a monthly schedule, the basic sequence is:

1. Calculate that month’s interest: opening balance × monthly rate.
2. Subtract the interest from the payment to determine the principal repaid.
3. Subtract principal repaid from the opening balance to get the next balance.

For example, at 8% APR the monthly rate is 0.6667%. On an opening balance of $20,000, the first month’s interest is about $133.33. With a $405.53 payment, about $272.20 goes toward principal. Later months calculate interest on the lower remaining balance. The figures are rounded here for illustration.

How to Read the Results

The monthly payment is the scheduled amount under the stated assumptions. Total interest is the estimated cost of borrowing above the principal, over the full schedule. It is not the total amount repaid: estimated principal plus interest is $24,331.80 in the worked example, before any excluded charges.

In an actual amortization schedule, each payment is divided between interest and principal. The balance after a payment can be calculated from the schedule’s prior balance, or directly for an idealized schedule as P(1 + r)^k − Payment × [(1 + r)^k − 1] ÷ r, where k is the number of payments made. The calculator shown here focuses on payment and total interest, rather than producing each row of that schedule.

When This Calculation Applies—and Its Limits

This method fits a loan with a fixed APR, equal monthly payments, and a term stated in whole monthly periods. It can help explain how the payment and interest estimate relate to the amount, rate, and term. For the actual APR, payment dates, fees, and payoff amount, use figures from the lender’s disclosure or account statement; an advertised or quoted rate may not capture every cost.

The formula does not directly describe every loan structure. Variable-rate loans can change their payment or payoff path when the rate resets. Interest-only arrangements, irregular payment dates, balloon payments, and loans with changing installments need a schedule that reflects those terms. A payment that is late or missed also changes the balance and may affect charges; those outcomes are not modelled here.

Common Calculation Mistakes

• Using APR as the monthly decimal: An 8% annual APR is not 0.08 per month. For this formula, divide the percentage by 1200 to get 0.0066667 per month.
• Using years as the payment count: Convert years to months by multiplying by 12. A five-year monthly loan has 60 scheduled payments.
• Confusing reducing-balance interest with flat-rate interest: A flat-rate calculation applies interest to the original principal throughout, while this method recalculates it on the remaining balance. The results are not interchangeable.
• Assuming the displayed payment is the full borrowing cost: It excludes charges not entered into the calculator. Compare the underlying terms and complete cost information in the lender’s documents.
• Rounding every intermediate figure: Small rounding differences can accumulate over many payments. This calculator rounds the payment to cents and uses that rounded payment for its total-interest estimate.

Frequently Asked Questions

How do you calculate interest on a reducing-balance loan?
For each period, multiply the opening outstanding balance by the periodic interest rate. Subtract that interest from the payment; the remainder reduces principal. Repeat using the new balance for the next period.

Is reducing-balance interest the same as flat-rate interest?
No. Reducing-balance interest is charged on the principal still owed, which declines as principal is repaid. Flat-rate interest is calculated on the original principal, so it follows a different calculation.

Why does the interest portion of a payment change?
At a fixed rate, the balance usually declines over time. Because each period’s interest is calculated on that balance, less of a later payment goes to interest and more goes to principal.

Does total interest include fees?
No. This calculator estimates interest from principal, APR, and term only. Check the lender’s disclosed charges and repayment schedule for costs outside that calculation.

Will an extra payment reduce the interest?
Paying extra toward principal can change the balance and subsequent interest, but the effect depends on how the loan applies extra payments and whether terms or charges apply. This calculator assumes only the scheduled equal payments.

Can I use this for a variable-rate loan?
Only for a period in which the rate is known and treated as fixed. A rate change can alter later interest and payments, so a single fixed-rate calculation cannot predict the complete schedule.

This is estimate arithmetic for education; the lender’s disclosure gives the exact figures.

Related

• Front-End DTI Ratio: Formula and Calculator
• Front-End DTI Ratio Formula and Mortgage Calculator
• Front-End Debt-to-Income Ratio 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 | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2