Borrowing Limit from a Monthly Payment
Solve the level-payment formula for the principal instead. Paying 800,000 a month for twenty years at 4.5% supports a loan of about 126 million.
Your numbers
Borrowing limit
126,452,349
Total repaid
192,000,000
Interest
65,547,651
Formula
Borrowing limit = Payment you can manage × ((1 + Annual rate ÷ 1200) ^ (Years × 12) − 1) ÷ ((Annual rate ÷ 1200) × (1 + Annual rate ÷ 1200) ^ (Years × 12))
A higher rate shrinks the loan a given payment supports, sharply. On a variable rate, run it again with two points added.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Payment you can manageWhat you can comfortably hand over each month. | 800,000 | 0 and up |
| Annual rate (%)Interest quoted per year; the monthly rate is this over 12. | 4.5 | 0 ~ 30 |
| Years (yr)How many years the money stays put; compounding bites harder as this grows. | 20 | 1 ~ 50 |
Step by step
Quick reference table
Results when only Payment you can manage changes and everything else stays put.
| Payment you can manage | Borrowing limit | Total repaid | Interest |
|---|---|---|---|
| 400,000 | 63,226,175 | 96,000,000 | 32,773,825 |
| 600,000 | 94,839,262 | 144,000,000 | 49,160,738 |
| 800,000 | 126,452,349 | 192,000,000 | 65,547,651 |
| 1,200,000 | 189,678,524 | 288,000,000 | 98,321,476 |
| 1,600,000 | 252,904,699 | 384,000,000 | 131,095,301 |
What each result means
| Result | At default values |
|---|---|
| Borrowing limitThe principal that monthly payment can support. | 126,452,349 |
| Total repaidEverything handed over by the last payment — principal plus interest. | 192,000,000 |
| InterestThe interest earned or owed over the period. | 65,547,651 |
Common mistakes
A higher rate shrinks the loan a given payment supports, sharply. On a variable rate, run it again with two points added.
Glossary
- Payment you can manage
- What you can comfortably hand over each month.
- Annual rate
- Interest quoted per year; the monthly rate is this over 12.
- Years
- How many years the money stays put; compounding bites harder as this grows.
- Borrowing limit
- The principal that monthly payment can support.
- Total repaid
- Everything handed over by the last payment — principal plus interest.
- Interest
- The interest earned or owed over the period.
Frequently asked questions
Q. How is Borrowing Limit from a Monthly Payment calculated?
Borrowing limit = Payment you can manage × ((1 + Annual rate ÷ 1200) ^ (Years × 12) − 1) ÷ ((Annual rate ÷ 1200) × (1 + Annual rate ÷ 1200) ^ (Years × 12)) — Solve the level-payment formula for the principal instead. Paying 800,000 a month for twenty years at 4.5% supports a loan of about 126 million.
Q. Can you walk through an example?
With Payment you can manage 800,000, Annual rate 4.5%, Years 20yr, the answer is Borrowing limit 126,452,349.
Q. What do I need to enter?
Enter Payment you can manage, Annual rate, Years. 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 Payment you can manage moves the answer to Payment you can manage 400,000 → Borrowing limit 63,226,175 and Payment you can manage 1,600,000 → Borrowing limit 252,904,699. 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?
A higher rate shrinks the loan a given payment supports, sharply. On a variable rate, run it again with two points added.
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