calculate-loan

01 Loan payments

Loan Repayment Graph: See Payments and Balance Over Time

Calculator No. 01-6526 · Updated · Formula and assumptions shown below

Monthly payment $405.53
Total interest
$4,331.67
= Monthly payment × loan term × 12 − loan amount
Loan amount
$20,000
Input
Interest rate (APR)
8 %
Input
You enter
Loan amount ($), Interest rate (APR) (%), Loan term (years)
You get
Monthly payment ($), Total interest ($)
Rounding
2 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

A loan repayment graph shows how scheduled payments, interest, and the remaining balance change over a loan’s term. Enter the loan amount, annual percentage rate (APR), and term in the calculator to estimate the monthly payment and total interest; use the graph alongside those figures to understand the repayment path.

Formula

The calculator estimates the fixed monthly payment on a fully amortizing loan, then estimates total interest by subtracting the original principal from the sum of all scheduled payments. It uses the standard level-payment formula:

Monthly payment = P × r ÷ [1 − (1 + r)−n]

  • P is the amount borrowed, in dollars.
  • r is the monthly interest rate, calculated as APR ÷ 1,200. APR is entered as a percentage per year.
  • n is the number of monthly payments, calculated as years × 12.
  • Total interest = monthly payment × n − P, in dollars. The calculation uses the payment rounded to cents.

A repayment graph commonly plots the outstanding balance against time, or separates each payment into principal and interest. The calculator’s two outputs supply useful summary figures for interpreting such a graph, but they do not create a plotted chart here.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a five-year term.

  1. Convert the APR to a monthly rate: 8 ÷ 1,200 = 0.0066667, or about 0.66667% per month.
  2. Find the number of payments: 5 × 12 = 60.
  3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)−60] = approximately $405.53 per month, rounded to cents.
  4. Calculate total interest using that rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

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

Assumptions

  • The interest rate remains fixed for the whole term.
  • Payments are made monthly, in equal amounts, at the end of each monthly period.
  • Interest accrues monthly using APR divided by 12; this is a simplified standard amortization assumption.
  • The estimate excludes fees, taxes, insurance, private mortgage insurance, and escrow because none is an input.
  • The loan is repaid through the scheduled payments, with no extra payments, missed payments, or changes to the balance.

How to Read a Loan Repayment Graph

On a balance-over-time graph, the horizontal axis usually represents months or years, and the vertical axis represents the remaining principal. The balance generally declines as payments are made. With a fixed rate and level monthly payments, the curve often falls more slowly at first and more quickly later: early payments allocate a larger share to interest, while later payments allocate more to principal.

A payment-breakdown graph may instead show two series or stacked portions for principal and interest. The total payment stays level under the calculator’s assumptions, but its composition changes. Interest is calculated on the balance still owed, so reducing principal reduces the interest charged in later periods. A lender’s own schedule may differ if its method, payment dates, or rounding rules differ.

When to Use the Estimate

Use the figures to understand the basic payment pattern or to compare hypothetical loan amounts, terms, and APR inputs. Each change affects the result differently. A larger principal generally raises the payment; a higher APR raises the interest portion and usually the payment; and a longer term generally spreads repayment across more months. A longer term can also increase total interest even when the monthly payment is lower.

Enter the figures that apply to the loan being examined. APR and fees are not universal constants: obtain the relevant rate and any charges from the lender’s written information. If the rate is variable, a single fixed-rate calculation cannot show future adjustments. For a detailed repayment graph, request or use a payment schedule that lists each period’s opening balance, interest, principal paid, and closing balance.

Common Misreadings and Limits

  • Payment is not the full borrowing cost. The monthly payment here excludes charges and costs that are not inputs. Total interest is not the same as every possible loan expense.
  • APR is not entered as a decimal. Enter 8 for 8%, not 0.08. The formula converts the percentage to a monthly rate by dividing by 1,200.
  • Rounding affects totals. Payments are rounded to cents, then multiplied by the number of months. A lender’s payment schedule may have small differences from its rounding and payment conventions.
  • The model assumes a fixed rate and regular payments. It does not model introductory rates, rate changes, skipped payments, extra payments, late charges, or a final adjusted payment.

One common misconception is that every payment reduces principal by the same amount. In a typical fixed-payment amortization schedule, the payment amount is level but the principal portion changes over time; the interest portion is based on the outstanding balance.

Frequently Asked Questions

What does a loan repayment graph show?
A repayment graph visualizes a loan’s progress, usually showing the outstanding balance over time or the principal and interest portions of each payment. The exact information depends on the graph’s axes and legend.

Why does the balance fall slowly at first?
When a loan balance is relatively high, interest takes a larger share of a level payment. As principal is paid down, less interest accrues and more of each later payment can reduce principal, assuming the rate and payment remain fixed.

Does a longer loan term reduce total interest?
Not necessarily. A longer term often reduces the amount due each month by spreading payments out, but it also gives interest more time to accrue. The result depends on the principal, APR, and repayment structure.

Can I use this calculator for a variable-rate loan?
It can show a hypothetical estimate for one fixed APR, but it cannot forecast a variable rate. A changing rate can alter both the required payment and the repayment schedule.

Why might my lender’s payment differ?
The lender may use different payment dates, interest accrual conventions, fees, or rounding rules. Check the loan disclosure or amortization schedule for the contractual figures and assumptions.

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

Related

Formula used
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

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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