Payoff Time with Extra Payments
Payoff Time with Extra Payments
How many years it takes to retire a loan when a fixed extra amount is added to every payment. The combined payment is treated as the annuity payment and the term solved for.
When to use: Use to see how much a round-up on each payment shortens a mortgage or car loan. Pair it with Total Interest Cost to see the interest saved.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PayoffYears | Years to Payoff | Years until the balance reaches zero | years |
| PV | Loan Balance | Current loan balance | $ |
| PMT | Required Payment | Scheduled periodic payment | $ |
| Extra | Extra Payment | Additional amount paid every period | $ |
| k | Interest Rate | Annual interest rate | % |
| m | Payments per Year | Number of payments per year | integer |
Real-Life Examples
Example 1: $200 Extra on a Mortgage
A $300,000 mortgage at 6.5% with a required payment of $1,896.20. The borrower pays $2,096.20 every month instead. Years to payoff?
Given
Step-by-Step
An extra $200 a month, about 10% more, cuts a 30-year mortgage to 23 years and saves roughly $85,000 of interest.
Example 2: $100 Extra on a Car Loan
A $25,000 car loan at 7% with a $495.03 payment, paid at $595.03 instead.
Given
Step-by-Step
The five-year loan is gone in four years, about a fifth sooner, for a fifth more per month.
Frequently Asked Questions
Every extra dollar goes straight to principal, and principal repaid early stops accruing interest for the rest of the term. The effect compounds in the borrower's favour.
Then the balance never falls and there is no payoff date; the formula returns an error. The combined payment must exceed one period's interest on the balance.