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
| Input | Default | Accepted range |
|---|---|---|
| PrincipalThe money you put in — the base that earns interest. | 3,000,000 | 0 and up |
| Annual rate (%)Interest quoted per year; the monthly rate is this over 12. | 19.9 | 0 and up |
| Monthly paymentWhat you owe every month. | 300,000 | 0 and up |
Step by step
Quick reference table
Results when only Principal changes and everything else stays put.
| Principal | Months (mo) | Interest | Total repaid |
|---|---|---|---|
| 1,500,000 | 5.3 | 78,802 | 1,578,802 |
| 2,250,000 | 8.1 | 172,594 | 2,422,594 |
| 3,000,000 | 11 | 307,322 | 3,307,322 |
| 4,500,000 | 17.4 | 716,958 | 5,216,958 |
| 6,000,000 | 24.5 | 1,350,157 | 7,350,157 |
What each result means
| Result | At 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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