Loan Payment Calculator

How to Calculate Loan Payments

The Loan Payment Calculator is an essential tool for anyone considering taking out a loan. It helps you estimate your monthly payments based on the loan amount, interest rate, and loan term. Understanding how loan payments are calculated can help you make informed decisions about borrowing and budgeting.

Loan Payment Formula

The formula for calculating the monthly payment on an amortized 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 ÷ 12 ÷ 100)
• n = Total Number of Payments (Loan Term in Months)

Calculation Steps

1. Determine the loan amount (L).
2. Convert the annual interest rate to a monthly rate (r) by dividing it by 12 and 100.
3. Calculate the total number of payments (n) by multiplying the loan term in years by 12 (if the term is in years).
4. Use the formula to calculate the monthly payment (P).
5. Multiply the monthly payment by the total number of payments to get the total amount paid.
6. Subtract the original loan amount from the total amount paid to get the total interest paid.

Example Calculation

Let's calculate the monthly payment for a loan with the following parameters:

• Loan Amount (L) = $250,000
• Annual Interest Rate = 3.5%
• Loan Term = 30 years

Step 1: Calculate the monthly interest rate

$$r = \frac{3.5\%}{12 \times 100} = 0.002916667$$

Step 2: Calculate the total number of payments

$$n = 30 \times 12 = 360$$

Step 3: Apply the monthly payment formula

$$P = 250,000 \times \frac{0.002916667(1+0.002916667)^{360}}{(1+0.002916667)^{360}-1}$$

$$P = 1,122.61$$

Step 4: Calculate total payments

$$\text{Total Payments} = 1,122.61 \times 360 = 404,139.60$$

Step 5: Calculate total interest paid

$$\text{Total Interest} = 404,139.60 - 250,000 = 154,139.60$$

Final Result:

• Monthly Payment: $1,122.61
• Total Interest Paid: $154,139.60
• Total Amount Paid: $404,139.60

Visual Representation

This diagram illustrates the amortization of a $250,000 loan over 30 years with a 3.5% annual interest rate. The blue area represents the remaining principal balance, which decreases over time as payments are made. The purple area shows the cumulative interest paid, which increases over the life of the loan. This visual representation helps to understand how the loan balance decreases and the total interest paid increases over the loan term.