# Present Value of a Single Sum of Money

Present value of a future single sum of money is the value that is obtained when the future value is discounted at a specific given rate of interest. In the other words present value of a single sum of money is the amount that, if invested on a given date at a specific rate of interest, will equate the sum of the amount invested and the compound interest earned on its investment with the face value of the future single sum of money.

## Formula

The formula to calculate present value of a future single sum of money is:

Present Value (PV) = | Future Value (FV) |

(1 + i)^{n} |

Where, **i** is the interest rate per compounding period which equals the annual percentage rate divided by the number compounding periods in one year; and **n** is the number of compounding periods.

1/(1+i)^{n} is called the present value factor.

## Examples

**Example 1:** Calculate the present value on Jan 1, 2011 of $1,500 to be received on Dec 31, 2011. The market interest rate is 9%. Compounding is done on monthly basis.

__Solution__

We have, Future Value

FV= $1,500 Compounding Periodsn= 12 Interest Ratei= 9%/12 = 0.75% Present ValuePV= $1,500 / ( 1 + 0.75% )^12 = $1,500 / 1.0075^12 ≈ $1,500 / 1.093807 ≈ $1,371.36

**Example 2:** A friend of you has won a prize of $10,000 to be paid exactly after 2 years. On the same day, he was offered $8,000 as a consideration for his agreement to sell the right to receive the prize. The market interest rate is 12% and the interest is compounded on monthly basis. Help him by determining whether the offer should be accepted or not.

__Solution__

Here you will compute the present value of the prize and compare it with the amount offered to your friend. It will be good to accept the offer if the present value of the prize is less than the amount offered.

So, Future Value

FV= $10,000 Compounding Periodsn= 2 × 12 = 24 Interest Ratei= 12%/12 = 1% Present ValuePV= $10,000 / ( 1 + 1% )^24 = $10,000 / 1.01^24 ≈ $10,000 / 1.269735 ≈ $7,875.66

Since the present value of the prize is less than the amount offered, it is good to accept the offer.

by Irfanullah Jan, ACCA and last modified on