How long will it take to pay off a balance?

When the payment is fixed and the term is what you want to know, solve for n.

Problem

You owe $12,000 on a card charging 22.9% a year and pay $400 a month. How many payments until it’s gone?

Keystrokes

fFINx≷y
0.00
Start clean.
22.9g12÷i
1.91
The monthly rate.
12000PV
12,000.00
The balance you owe.
400CHSPMT
−400.00
Your monthly payment, negative because you pay it.
n
45.00
Solves for the number of payments.
FV
17.99
With n now a whole number, shows how much the last payment overshoots.

Answer

It takes 45 payments. The last one is $17.99 less than $400, because a full payment would overpay by that much.

Why n is a whole number

A financial calculator rounds n up to the next whole period, because you can’t make part of a payment period. The exact answer here is a little under 45, so the final payment is smaller.

Pressing FV with n stored as a whole number shows that difference. It’s positive because it’s money that would come back to you if you paid the full $400 the last time.

What if the payment is too small?

If the payment doesn’t cover the monthly interest, the balance never falls and the calculator shows an error. At 22.9%, the interest on $12,000 is about $229 a month, so any payment below that never pays it off.

Questions

How much interest will I pay?

Multiply the payment by n and subtract the balance: RCL PMT RCL n × RCL PV +. Then subtract the overshoot shown by FV.