# How to Calculate a Simple Interest Payment

Simple interest loans are common in everything from a home mortgage to a personal loan. With a simple interest loan, the amount you're borrowing is the principal, the length of the loan is the term, the money you pay for the privilege of borrowing is the interest and the date on which the loan is to be paid in full is its maturity date. Although you can use a calculator to determine a simple interest payment, understanding what's behind this calculation is a useful money management skill.

## The Formula

The simple interest formula is I = PRT:

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• I is the amount of interest expressed as a dollar value
• P is the principal
• R is the annual rate of interest
• T is the loan term expressed in years or a fraction of a year

For example, if you borrow \$5,000 at a 5 percent annual interest rate for one year, you'll pay \$5,250 -- \$5,000 x 0.05 x 1 -- on the maturity date.

In the same way, if you borrow \$3,000 at a 5 percent annual interest rate for six months, you'll pay \$3,075 -- \$3,000 x 0.05 x 6/12 -- on the maturity date.

## Step 1: Calculate a Monthly Payment

The formula is P/loan term in months.

The monthly payment on a 12-month, \$5,000 loan will be \$5,000/12 or \$416.67 each month.

The monthly payment on a six-month, \$3,000 loan will be \$3,000/6 or \$500 each month.

## Step 2: Calculate Monthly Interest

The monthly interest on a \$5,000 loan at a 5 percent annual interest rate for one year will be \$5,000 x 0.05 x 1/12 or \$20.83.

The monthly interest on a \$3,000 loan at a 5 percent annual interest rate for six months will be \$3,000 x 0.05 x 1/12 or \$12.50.

## Step 3: Determine the Total Monthly Payment

Add the monthly principal and interest payment to get the monthly loan payment:

• The monthly loan payment on a \$5,000 at a 5 percent annual interest rate for one year will be \$416.67 + 20.83 or \$437.50.
• The monthly loan payment on a \$3,000 at a 5 percent annual interest rate for six months will be \$500 + \$12.50 or \$512.50.

## Calculate a Short-term Loan Payment

You'll need to convert days into a portion of a year to calculate the payment on a short-term loan with a maturity date measured in days rather than months. These loans are usually paid in a lump sum on the maturity date.

## Step 1: Convert Days to a Portion of a Year

The formula is the number of days/365 or 366 days for a leap year:

• A 90-day loan based on 365 days is 0.25 of one year
• A 180-day loan based on 366 days is 0.49 of one year

## Step 2: Calculate total Interest

The formula is P x I x T:

• The interest on a 90-day \$3,000 loan at a 5 percent annual interest rate will be \$3,000 x 0.05 x 0.25, or \$37.50.
• The interest on a 180-day \$3,000 loan based on 366 days at a 5 percent annual interest rate will be \$3,000 x 0.05 x 0.49, or \$73.50.

## Step 3: Determine the Total Amount Owed

Add the principal and interest to get the amount owed as of the maturity date.