Loan Payment Calculator

What is a Loan Payment Calculator?

A Loan Payment Calculator is a financial tool that helps borrowers estimate the monthly payments on a loan. It takes into account the loan amount, interest rate, and loan term to provide an accurate estimate of how much you'll need to pay each month to fully repay the loan by the end of its term.

The Loan Payment Formula

The formula used to calculate the monthly payment on a loan is:

\[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]

Where:

• \(P\) = Monthly payment
• \(L\) = Loan amount
• \(r\) = Monthly interest rate (annual rate divided by 12)
• \(n\) = Total number of months in the loan term

Step-by-Step Loan Payment Calculation

1. Convert the annual interest rate to a monthly rate: \[r = \frac{\text{Annual Rate}}{12}\]
2. Determine the total number of monthly payments: \[n = \text{Loan Term in Years} \times 12\]
3. Apply the loan payment formula: \[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]
4. Calculate total repayment: \[\text{Total Repayment} = P \times n\]
5. Calculate total interest: \[\text{Total Interest} = \text{Total Repayment} - L\]

Example Calculation

Let's calculate the monthly payment for a $200,000 loan at 4% annual interest for 30 years:

1. \(r = \frac{4\%}{12} = 0.3333\%\) per month
2. \(n = 30 \times 12 = 360\) months
3. \(P = 200000 \times \frac{0.003333(1+0.003333)^{360}}{(1+0.003333)^{360}-1} = $954.83\)
4. Total Repayment = $954.83 × 360 = $343,739.80
5. Total Interest = $343,739.80 - $200,000 = $143,739.80

Visual Representation

This chart shows the proportion of principal ($200,000) to total interest ($143,739.80) for the example loan.