Simple Loan Calculator

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Simple Loan Calculator

Loan Amount:

Interest Rate:

Loan Term:

Answer:

Monthly Payment = $ 377.42

Total Interest Paid = $ 2,645.48

Create an Amortization Schedule

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Calculator Use

Use this simple loan calculator for a calculation of your monthly loan payment. The calculation uses a loan payment formula to find your monthly payment amount including principal and compounded interest.

Input loan amount, interest rate as a percentage and length of loan in years or months and we can find what is the monthly payment on your loan.

This loan calculator also lets you create and print a loan amortization schedule. An amortization schedule lists all of your loan payments over time. The schedule breaks down each payment so you can see for each month how much you'll pay in interest, and how much goes toward your loan principal.

What Factors are Involved in Loan Calculations?

It's important to understand how much you'll need to repay your lender when you borrow money. Understanding how interest is figured will help you make wise choices when shopping for a loan. These factors are used in loan calculations:

Principal - the amount of money you borrow from a lender
Interest - the cost of borrowing money, paid in addition to your principal. You can also think of it as what you owe your lender for financing the loan.
Interest rate - the percentage of the principal that is used to calculate total interest, typically a yearly % rate.
Loan term - how long it will take you to pay back the loan, for example 4 or 5 years for a car loan, or 30 years for a home loan.

The Loan Payment Formula

Loans like car loans or home mortgages are typically calculated using a compounding formula to find the monthly payment amount. "Compounded interest" means that interest is calculated on both principal and unpaid interest from previous periods. It may seem complicated but exponents in the formula simplify the math.

The formula to calculate monthly loan payment is:
P x i(1 + i)ⁿ / (1 + i)ⁿ - 1

Written in standard math notation, the loan payment equation looks like this:

$ \text{Payment}=\dfrac{P \times i(1+i)^n}{(1+i)^n-1} $

The variables in the loan payment formula and equation are:

Payment = Monthly loan payment amount
P = Principal, or loan amount
i = Annual interest rate as a monthly decimal rate (annual interest rate% / 100 / 12)
n = Length of loan in number of months

So using these variables you would read the equation as, "Monthly payment equals one plus interest rate as a decimal, raised to the n^th power, times interest rate, times P, all divided by one plus interest rate, raised to the n^th power, minus one."

How to Calculate the Monthly Loan Payment

Using the loan payment formula plug in your known values for interest and time. Interest should be a decimal as a monthly rate so divide your percentage by 100 and then by 12 to get interest as a monthly decimal interest rate.

For example, if your annual interest rate was 5.3%, divide that by 100 to get interest as a decimal.

i = I% / 100
i = 5.3% / 100
i = 0.053

If you have an annual interest rate you should also divide that by 12 to get the decimal interest rate per month.

i_monthly = i / 12
i_monthly = 0.053 / 12
i_monthly = 0.00441667

For this formula, time should be in months, so if your loan term is in years just multiply years by 12. For example, if your loan term was 5 years, mulitply by 12 to get the term in months.

term = years * 12
term = 5 years * 12
term = 60 months

Calculate your monthly payment on a loan of $18,000 given interest as a monthly decimal rate of 0.00441667 and term as 60 months.

i_monthly = 5.3% / 100 / 12 = 0.00441667 decimal interest rate per month
n = 5 × 12 = 60 months

Then using the formula insert these values:

$ \text{Payment}=\dfrac{\text{Amount} \times i(1+i)^n}{(1+i)^n-1} $

$ =\dfrac{(\$18,000)(0.00441667)(1+0.00441667)^{60}}{(1+0.00441667)^{60}-1} $

$ =\dfrac{(\$18,000)(0.00441667)(1.30267)}{1.30267-1} $

$ =\dfrac{(\$18,000)(0.00575346)}{0.30267} $

$ =\dfrac{103.562}{0.30267} $

$ =\$342.16 $

So for a loan of $18,000 for 60 months with an annual interest rate of 5.3%, your monthly payment would be $342.16.

Calculate Total Interest Paid on a Loan

Calculate total amount paid including interest by multiplying the monthly payment by total months. To calculate total interest paid subtract the loan amount from the total amount paid. This calculation is accurate but may not be exact to the penny since some actual payments may vary by a few cents.

Using the example loan information above $342.16 × 60 months = $20,529.60 total amount paid with interest. Now subtract the original loan amount from the total paid including interest:
$20,529.60 - $18,000.00 = 2,529.60 total interest paid

This simple loan calculator lets you do a quick assessment of payments given various interest rates and loan terms. If you'd like to experiment with loan variables or need to find interest rate, loan principal or loan term, use our standard Loan Calculator.

This calculator also assumes interest compounding occurs monthly. For weekly, quarterly or daily interest compounding options see our Advanced Loan Calculator.

Example Loan Payment Calculation

Suppose you take a $20,000 loan for 5 years at 5% annual interest rate.

n = 5 × 12 = 60 months
i = 5% / 100 / 12 = 0.004167 interest rate per month

Then using the formula with these values:

$ \text{Payment}=\dfrac{\text{Amount} \times i(1+i)^n}{(1+i)^n-1} $

$ =\dfrac{(\$20,000)(0.004167)(1+0.004167)^{60}}{(1+0.004167)^{60}-1} $

$ =\$377.42 $

Total Interest Paid on a Loan

Multiply your monthly payment by total months of loan to calculate total amount paid including interest. Then subtract the original loan amount from the total amount paid to to find the total interest paid.

$377.42 × 60 months = $22,645.20 total amount paid with interest
$22,645.20 - $20,000.00 = 2,645.20 total interest paid