# Loan Payment Calculator

 Rate per Period**: % Number of Periods: Present Value: \$ Payment Due at: beginning end of period Payment Amount: \$

## **Loan Payment Calculations:

Calculates payments on a loan based on constant payments at a constant interest rate. Assumes you want the Future value of the loan to equal 0.

Rate per Period is the interest rate for each payment period. Number of Periods is the total number of payment periods. Make sure that you are consistent with the units (months, years or quarters) you use for specifying Rate per Period and Number of Periods.

Payment Amount is the payment made each period. If you are paying \$413.00 per payment then the answer will be (-413.00).

Present Value is the lump-sum amount that a series of future payments is worth right now. For example, if you borrow \$10,000 the present value to you is \$10,000.

How to Calculate APR: Acronym for Annual Percentage Rate. The Effective Annual Interest Rate. The actual amount of interest for each year. You should be able to get a basic understanding from Wikipedia for Annual Percentage Rate and Nominal Interest Rate.

You will have to be sure you are using the right interest rate so that the calculations are correct for your situation. See the following explanation.

A loan with a Nominal Interest Rate of 7% compounded monthly will have a higher Effective Annual Interest Rate than a loan with an APR of 7% compounded monthly.

• If the Nominal Interest Rate (also known as the "Stated Rate") for your loan is stated as 7% compounded monthly then the APR will be about 7.22%. A nominal interest rate of 7% will become 7%/12 months = 0.583% per month (0.07/12 months = 0.00583 per month). Compounding monthly (1 + 0.00583)^12 = 1.0722 which becomes 1.0722 - 1 = 0.0722 = 7.22%.
• If the APR for your loan is stated as 7% compounded monthly then the APR will be 7%. An APR of 7% will become 12√(1 + 0.07) = 1.00565 or 1.00565 - 1 = 0.00565 = 0.565% per month. Compounding monthly (1 + 0.00565)^12 = 1.07 which becomes 1.07 - 1 = 0.07 = 7%.
• For more detailed information on loan and investment formulas see this good practical treatment by Stan Brown at Oak Road Systems: http://oakroadsystems.com/math/loan.htm

## Example Future Value Calculations:

You have \$500 savings and will start to save \$225 per month in an account that yields 15% per year. You will make your deposits at the end of each month. You want to know the value of your investment in 5 years or, the future value of your savings account.

• Rate per period = 15% / 12 = 1.25%
• Number of Periods = 5 (years) / 12 (months/ year) = 60 (months)
• Payment Amount = -225.00 (money you pay out is negative and money you recieve is positive)
• Present Value = -500 (money you already paid to the account.
• Payment is Due at the end of each period
• At the end of 5 years your savings account will be worth \$20982.85

You took a loan for \$10,000 at a Nominal Interest Rate of 15% and want to know how much you will still owe in 4 years if you pay \$125 at the end of each month.

• Rate per period = 15% / 12 = 1.25%
• Number of Periods = 4 (years) / 12 (months/ year) = 48 (months)
• Payment Amount = -125.00 (money you pay out is negative and money you recieve is positive)
• Present Value = +10,000 (money you recieved, the loan).
• Payment is Due at the end of each period
• At the end of 4 years you will still owe \$10,000. You are essentially paying the interest only. You had better up your payments if you ever want to get out of debt.

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