# Present Value Calculator

 Interest Rate per Period: % Number of Periods: Payment Amount: \$ Future Value: \$ Payment Due at Period: beginning end Present Value: \$ 0

Calculates the present value of an annuity for a future value based on periodic, constant payments and a constant interest rate. The present value is the total amount that a series of future payments is worth now.

## Present Value Formula:

Where pv = present value, fv = future value, rate = rate per period, nper = number of periods, pmt = payment amount, and type = 1 if payments are made at the beginning of each period or type = 0 if payments are made at the end of each period..

pv = [ -pmt * (1 + rate * type) * [ ( (1 + rate)^nper - 1) / rate] - fv ] / (1 + rate)^nper

### **Notes on Present Value Calculations:

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 you use for specifying Rate per Period and Number of Periods. If you make monthly payments on a 3 year loan the number of periods is 36 and the interest rate you should specify is the monthly rate not the yearly rate. If the yearly Nominal Interest Rate is 15% and you are making monthly payments then your Rate per Period is 15% / 12 = 1.25%. Read about APR below.

Payment Amount is the payment made each period. Enter a negative number. If you are paying \$263.00 per payment then enter (-263.00).

Future Value is the future value, or a cash balance you want to attain after the last payment is made. The future value of a loan, for example, is 0. However, if you want to save \$10,000, then \$10,000 is the future value. You could make a guess at an interest rate to calculate how much you must save each month.

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