How much faster do extra payments pay off a mortgage?

Add the extra amount to the payment and solve for the number of payments.

Problem

On a $350,000, 30-year mortgage at 6.5%, you pay $300 extra every month. When is it paid off?

Keystrokes

fFINx≷y
0.00
Start clean.
30g12×n
360.00
The original 360 payments.
6.5g12÷i
0.54
Monthly rate.
350000PV
350,000.00
The amount borrowed.
PMT
−2,212.24
The required payment.
300−PMT
−2,512.24
Adds $300 to what you pay (more negative) and stores it as the new payment.
n
261.00
The number of payments at the higher amount.
12÷
21.75
In years.

Answer

Paying $2,512.24 instead of $2,212.24 pays the loan off in 261 payments, about 21.75 years instead of 30.

Why it works

The payment is negative, so subtracting 300 makes it larger in the direction of money out. PMT stores it, and n counts how many of those payments it takes to bring the balance to zero.

The calculator rounds n up to a whole payment, so the last payment is a little smaller. FV after this shows by how much.

How much interest it saves

Interest is charged on the balance. Every extra dollar paid early stops earning the lender 6.5% a year for the rest of the loan, so early extra payments save the most.

Questions

What about a single lump-sum payment?

Use the remaining-balance guide to find the balance on that date, subtract the lump sum, store it as PV with the original payment, and solve for n.