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Months to Pay It Off

This asks the reverse question: with the payment fixed, how long? When the payment sits only a little above one month of interest, the term stretches out dramatically, because the balance hardly moves.

Your numbers

Months

11mo

Interest

307,322

Total repaid

3,307,322

Formula

Months = −ln(1 − Principal × i ÷ Monthly payment) ÷ ln(1 + i)

Revolving credit that charges a percentage of the balance shrinks the payment too, so it takes far longer than this. These figures assume a fixed amount every month.

What to enter

InputDefaultAccepted range
PrincipalThe money you put in — the base that earns interest.3,000,0000 and up
Annual rate (%)Interest quoted per year; the monthly rate is this over 12.19.90 and up
Monthly paymentWhat you owe every month.300,0000 and up

Step by step

FormulaMonths = −ln(1 − Principal × i ÷ Monthly payment) ÷ ln(1 + i)
With the default numbersMonths = −ln(1 − 3,000,000 × i ÷ 300,000) ÷ ln(1 + i)
AnswerMonths = 11 mo

Quick reference table

Results when only Principal changes and everything else stays put.

PrincipalMonths (mo)InterestTotal repaid
1,500,0005.378,8021,578,802
2,250,0008.1172,5942,422,594
3,000,00011307,3223,307,322
4,500,00017.4716,9585,216,958
6,000,00024.51,350,1577,350,157

What each result means

ResultAt default values
Months (mo)The period counted in months; a yearly rate gets divided by twelve.11
InterestThe interest earned or owed over the period.307,322
Total repaidEverything handed over by the last payment — principal plus interest.3,307,322

Common mistakes

Revolving credit that charges a percentage of the balance shrinks the payment too, so it takes far longer than this. These figures assume a fixed amount every month.

Glossary

Principal
The money you put in — the base that earns interest.
Annual rate
Interest quoted per year; the monthly rate is this over 12.
Monthly payment
What you owe every month.
Months
The period counted in months; a yearly rate gets divided by twelve.
Interest
The interest earned or owed over the period.
Total repaid
Everything handed over by the last payment — principal plus interest.

Frequently asked questions

Q. How is Months to Pay It Off calculated?

Months = −ln(1 − Principal × i ÷ Monthly payment) ÷ ln(1 + i) — This asks the reverse question: with the payment fixed, how long? When the payment sits only a little above one month of interest, the term stretches out dramatically, because the balance hardly moves.

Q. Can you walk through an example?

With Principal 3,000,000, Annual rate 19.9%, Monthly payment 300,000, the answer is Months 11mo.

Q. What do I need to enter?

Enter Principal, Annual rate, Monthly payment. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only Principal moves the answer to Principal 1,500,000 → Months (mo) 5.3 and Principal 6,000,000 → Months (mo) 24.5. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

Revolving credit that charges a percentage of the balance shrinks the payment too, so it takes far longer than this. These figures assume a fixed amount every month.

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