220.2713 months is the example result. A payment that does not exceed monthly interest cannot amortise the balance. The model assumes the payment and rate remain fixed.
A payment that does not exceed monthly interest cannot amortise the balance.
Comparing financial amounts on a defined basis
A payment that does not exceed monthly interest cannot amortise the balance. The model assumes the payment and rate remain fixed. A financial model is useful when its cash amounts, rate convention and time horizon describe the same case. Interest, return and purchasing power are different outputs. A projection should remain separate from an observed or audited balance.
What the model includes
Payoff months = −ln(1 − monthly rate × balance ÷ payment) ÷ ln(1 + monthly rate). At zero interest, months = balance ÷ payment. Payment must exceed monthly interest. Check whether a rate is annual, monthly, simple or compounded. Enter fees only where the form represents them and identify contractual charges that remain outside the estimate. A monthly payment alone does not establish affordability or total ownership cost. Use the result to prepare the next question about terms or assumptions. Tax treatment, lender conditions and valuation evidence require the relevant source documents; they cannot be recovered from a few numeric inputs.
Example with the supplied inputs
Current balance: 200000; Annual interest rate (%): 6; Monthly payment: 1500. Result: 220.2713 months. The values are illustrative.
Compare one changed input
Current balance changes from 200000 to 220000. The result becomes 265.0115 months. All other inputs remain fixed.
Calculation rule
Payoff months = −ln(1 − monthly rate × balance ÷ payment) ÷ ln(1 + monthly rate). At zero interest, months = balance ÷ payment. Payment must exceed monthly interest.
Inputs and output
| Input | Example value | Entry convention |
|---|---|---|
| Current balance | 200000 | Use current balance on the currency and period basis shown by the formula. Keep gross amounts, net amounts and unit amounts distinct; the page does not fetch a price or exchange rate. |
| Annual interest rate (%) | 6 | Enter annual interest rate (%) on the percentage scale used in the formula (20 means 20%, not 0.20). Keep its base and reporting period consistent with the other inputs. |
| Monthly payment | 1500 | Use monthly payment on the currency and period basis shown by the formula. Keep gross amounts, net amounts and unit amounts distinct; the page does not fetch a price or exchange rate. |
Output: 220.2713 months is the example result. A payment that does not exceed monthly interest cannot amortise the balance. The model assumes the payment and rate remain fixed. Unit: months.
How to use the page
Collect the inputs
Gather Current balance, Annual interest rate (%), Monthly payment. Use one period and the units shown in the form.
Run the calculation
Enter the values and select the action. The calculation rule above explains how the inputs produce the result.
Compare a scenario
Change Current balance on its own, keeping the other inputs fixed. Read both results before changing another assumption.
Worked example
With the example inputs listed above, the result is 220.2713 months.
Change Current balance from 200000 to 220000 while keeping every other value fixed. The result becomes 265.0115 months. This comparison isolates that input; it does not forecast how other variables will respond.
Check the stated formula, units and limits before using the result in a decision.
Keep the displayed formula, input units and model scope with the result. Corrections or questions can be sent through the request section on this page.