Calculator Soup^{®}

Of the four variables in this loan calculation, (Loan Amount, Interest Rate, Number of Months, and Monthly Payment) if you know any three you can calculate the fourth. Also create amortization schedules for the results. For other options use the advanced loan calculator.

- Loan Amount
- the original principal on a new loan or principal outstanding if you are calculating on a current loan
- Interest Rate
- the annual nominal interest rate or stated rate on the loan
- Number of Months
- number of months which coincides with the number of payments to repay the loan
- Monthly Payment
- the amount to be paid on this loan on a monthly basis
- Compounding
- compounding is assumed to occur monthly with payments. For other compounding options use the advanced loan calculator.

Use this loan calculator to determine your monthly payments, interest rate, or months or principal remaining on a current loan.

A loan is basically an annuity you are paying to the lending institution. In most cases payments are made at the end of each moth. So, we can apply the equation for present value of ordinary annuity when calculating the information we want to find.

\[ PV=\frac{PMT}{i}\left[1-\frac{1}{(1+i)^n}\right] \]where PV is Loan Amount, PMT is the Monthly Payment, n is the Number of Months and i is the interest rate per month in decimal (Interest Rate divided by 12).

**Find the Loan Amount **

To calculate the loan amount we use the equation as-is:

\[ PV=\frac{PMT}{i}\left[1-\frac{1}{(1+i)^n}\right] \]**Find the Interest Rate**

To find the interest rate the calculation is a complex process involving the Newton-Raphson Method.

**Find the Number of Months**

To find the number of months we solve for n:

\[ \Large\,n=\frac{ln\left[\frac{\frac{PMT}{i}}{\frac{PMT}{i}-PV}\right]}{ln(1+i)} \]**Find the Monthly Payment **

To find the monthly payment we solve the equation for PMT:

\[ PMT=\frac{PVi(1+i)^n}{(1+i)^n-1} \]**Cite this content, page or calculator as:**

Furey, Edward "Loan Calculator" From *http://www.CalculatorSoup.com* - Online Calculator Resource.