The formula to calculate the Number of Months (n) is:
\[ n = \log_{10}\left(\frac{p/R}{(p/R) - LA}\right) / \log_{10}(1 + R) \]
Where:
The number of months is the total number of compounding intervals.
The Monthly Payment is the amount a borrower is required to pay each month until a debt is paid off.
Interest Rate is the amount charged, expressed as a percentage of the principal, by a lender to a borrower for the use of assets.
The Loan Amount is the original principal on a new loan or principal remaining on an existing loan.
Let's assume the following values:
Using the formula:
\[ n = \log_{10}\left(\frac{28000 / 0.2}{(28000 / 0.2) - 20000}\right) / \log_{10}(1 + 0.2) \]
Evaluating:
\[ n = \log_{10}\left(\frac{28000 / 0.2}{(28000 / 0.2) - 20000}\right) / \log_{10}(1 + 0.2) \]
The Number of Months is 0.845487952921921.
| Monthly Payment | Interest Rate | Loan Amount | Number of Months |
|---|---|---|---|
| 27000 | 0.15% | 19000 | 0.798160672426192 |
| 27000 | 0.15% | 20000 | 0.842740403107894 |
| 27000 | 0.15% | 21000 | 0.887599632359059 |
| 27000 | 0.2% | 19000 | 0.831961891941756 |
| 27000 | 0.2% | 20000 | 0.879449763893723 |
| 27000 | 0.2% | 21000 | 0.927352382335187 |
| 27000 | 0.25% | 19000 | 0.867131746593110 |
| 27000 | 0.25% | 20000 | 0.917769800829427 |
| 27000 | 0.25% | 21000 | 0.968986588212764 |
| 27500 | 0.15% | 19000 | 0.782824725561863 |
| 27500 | 0.15% | 20000 | 0.826497436704025 |
| 27500 | 0.15% | 21000 | 0.870438354508371 |
| 27500 | 0.2% | 19000 | 0.815652077277409 |
| 27500 | 0.2% | 20000 | 0.862133838074074 |
| 27500 | 0.2% | 21000 | 0.909012883694103 |
| 27500 | 0.25% | 19000 | 0.849770733497738 |
| 27500 | 0.25% | 20000 | 0.899289691681861 |
| 27500 | 0.25% | 21000 | 0.949361945763682 |
| 28000 | 0.15% | 19000 | 0.768067556912658 |
| 28000 | 0.15% | 20000 | 0.810869421110351 |
| 28000 | 0.15% | 21000 | 0.853928870795223 |
| 28000 | 0.2% | 19000 | 0.799970555195475 |
| 28000 | 0.2% | 20000 | 0.845487952921921 |
| 28000 | 0.2% | 21000 | 0.891386253801249 |
| 28000 | 0.25% | 19000 | 0.833093213077319 |
| 28000 | 0.25% | 20000 | 0.881541469997783 |
| 28000 | 0.25% | 21000 | 0.930519226548771 |
| 28500 | 0.15% | 19000 | 0.753856978997976 |
| 28500 | 0.15% | 20000 | 0.795822047261370 |
| 28500 | 0.15% | 21000 | 0.838034698480483 |
| 28500 | 0.2% | 19000 | 0.784881646235582 |
| 28500 | 0.2% | 20000 | 0.829473883304061 |
| 28500 | 0.2% | 21000 | 0.874431634588744 |
| 28500 | 0.25% | 19000 | 0.817059492511287 |
| 28500 | 0.25% | 20000 | 0.864482370153117 |
| 28500 | 0.25% | 21000 | 0.912412453965791 |
| 29000 | 0.15% | 19000 | 0.740163149692521 |
| 29000 | 0.15% | 20000 | 0.781323514178644 |
| 29000 | 0.15% | 21000 | 0.822722030603901 |
| 29000 | 0.2% | 19000 | 0.770352326619413 |
| 29000 | 0.2% | 20000 | 0.814056262617403 |
| 29000 | 0.2% | 21000 | 0.858111238005429 |
| 29000 | 0.25% | 19000 | 0.801632902001729 |
| 29000 | 0.25% | 20000 | 0.848072904298523 |
| 29000 | 0.25% | 21000 | 0.894999198182547 |