Loan Calculator

The Loan Calculator calculates your monthly loan payment and amortization schedule based on the loan amount, loan length, and loan interest rate. Check out the charts and amortization schedule below to see how the interest and principal you pay each month changes and how that affects your loan balance over time.

How do you calculate your monthly loan payment?

If you're interested in learning about the math behind loans and amortization schedules, use the following amortization formula to calculate the monthly payment for a loan:

$$\textbf{Payment} = \frac{PV*i(1+i)^n}{(1+i)^n - 1}$$

Where:

• PV: Loan amount
• i: Monthly loan interest rate as a decimal or fraction, or annual loan interest rate divided by 12
• n: Length of the loan in months

Example

Let's use the amortization formula to calculate the monthly loan payment for the example above where:

• PV: $500,000
• i: .055/12
• n: 360

$$\textbf{Payment} = \frac{$500,000*\frac{0.055}{12}(1+\frac{0.055}{12})^{360}}{(1+\frac{0.055}{12})^{360} - 1}$$

$$ \phantom{\textbf{Payment}} = $2,838.95$$

How do you calculate an amortization schedule?

Now that we know the monthly loan payment, we can create an amortization schedule that breaks down how your payment is divided into principal and interest, and shows how much your total loan balance decreases each month. Let's find the interest, principal, and loan balance for the first two months of loan payments.

Month 1

First, we can calculate the interest paid during Month 1 by multiplying the current loan balance by the monthly loan interest rate:

$$\textbf{Interest} = $500,000 * (\frac{0.055}{12})$$

$$ \phantom{\textbf{Interest}} = $2,291.67$$

Next, we can subtract the Month 1 interest from the monthly loan payment to find the principal paid during Month 1:

$$\textbf{Principal} = $2,838.95 - $2,291.67$$

$$ \phantom{\textbf{Principal}} = $547.28$$

Finally, we can subtract the Month 1 prinicpal paid from the loan amount to find the loan balance after Month 1:

$$\textbf{Balance} = $500,000 - $547.28$$

$$ \phantom{\textbf{Balance}} = $499,452.72$$

Month 2

Like we did for Month 1, we can calculate the interest paid during Month 2 by multiplying the current loan balance by the monthly loan interest rate:

$$\textbf{Interest} = $499,452.72 * (\frac{0.055}{12})$$

$$ \phantom{\textbf{Interest}} = $2,289.16$$

Next, we can subtract the Month 2 interest from the monthly loan payment to find the principal paid during Month 2:

$$\textbf{Principal} = $2,838.95 - $2,289.16$$

$$ \phantom{\textbf{Principal}} = $549.79$$

Lastly, we can subtract the Month 2 prinicpal paid from the remaining loan amount to find the loan balance after Month 2:

$$\textbf{Balance} = $499,452.72 - $549.79$$

$$ \phantom{\textbf{Balance}} = $498,902.93$$

If you keep following these steps, you can calculate how the principal portion of your monthly payment increases and your overall loan balance decreases over time. Use the Loan Calculator above to see how monthly payments and total interest paid changes with different loan amounts and loan interest rates.